Circular Pathway

OAC is a circle of radius = r, there is pathway, outside the circle of width = W Area of circular pathway = πW (2r+W)

When, the pathway is inside the circle, Area of circular pathway = πW (2r - W) Examples:

1. If three sides of a triangle are 5, 6 and 7 cm respectively, find the area of triangle.

Sol: Area of  = s(s a)(s b)(s c)   W r

R W

A

O

C

A W r

W

C A W

W O

Now, s = a b c 5 6 7

2 2

     = 9

 Area = 9 (9 5)(9 6)(9 7)     9 4 3 2  

= 216 6 6 cm².

2. ABC is an equilateral triangle of side 24 cm. Find the in radius of the triangle.

Sol: In a equilateral triangle, the altitude, median and perpendicular are equal.

 AD = ³/2 x 24 = 12 ³

GD (in radius) = 1/3 x 12 ³ = 4 ³ cm

3. The base and other side of an isosceles triangle is 10 and 13 cm respectively. Find its area.

Sol: Area of Isosceles  = ^{b 4a2 b2}

4 

Given, base b = 10 Other side a = 13 Area (A) = ^{10 4 (13)2 102 10 676 100}

4    4 

= ¹⁰

4 24 = 60 cm².

4. In a right-angled triangle, the length of two legs are 12 and 5 cm. Find the length of hypotenuse and its area.

Sol: In a right angled triangle,

(Hypotenuse)² = (one leg)² + (other leg)²

= 12² + 5²

 Hypotenuse = 12²5² = 169 = 13 cm.

In a right angled triangle,

Area = ^{1 (leg)}₁ ^(leg)₂ ^{1 12 5}

2   2  = 30 cm².

5. If the perimeter and diagonal of a rectangle and 14 and 15 cm respectively.

Find its area.

Sol: In a rectangle,

(Perimeter)²

4 = (diagonal)2 + 2 x Area ; ⁽¹⁴⁾²

4 = (5)² + 2 x Area

 2 x Area = ¹⁹⁶

4 - 25  Area = ^{49 25}

2

 = 12 cm².

6. Find the length of the diagonal and the perimeter of a square plot if its area is 900 square metres.

Sol: In a square, A = ^{d2 p2}

2 16

 (Diagonal)² = 2 x Area = 900

 Diagonal (d) = 2 900 30   2 = 42.42 metres (Perimeter)² = 16 x Area = 16 x 900

 Perimeter (P) = 16 900 = 120 metres.

7. A field in the shape of a rhombus has the distances between pairs of

opposite vertices as 14 m and 48 m. What is the cost (in rupees) of fencing the field at Rs.20 per metre?

Sol: The diagonals are 14 m and 48 m

Sides of rhombus = ^{14 2 48 2 625}

2 2

    

   

    = 25

Perimeter of rhombus = 4 x 25 = 100 m.

Cost of fencing the field = 100 x 20 = Rs.2000

8. In a trapezium, the length of parallel sides are 20 and 25 metres

respectively and the perpendicular distance between the parallel sides is 12 metres. Find the area of trapezium.

Sol: One parallel side a = 20 metres. Second parallel side b = 25 metres.

Height (perpendicular distance between a and b) = 12 metres.

Area = ¹(a b) h ¹(20 25) 12

2   2   = 270 m².

9. The distance between a pair of opposite vertices of a quadrilateral is 32 units. The lengths of the perpendiculars drawn on to this diagonal from the other two vertices are 4 1/3 units and 6 2/3 units respectively. Find the area (in sq units) of the quadrilateral?

Sol: Area of quadrilateral = 1/2 x 32 x ^{13 20}

3 3

  

 

  = 178 sq units.

A B

C D

10.

In the above parallelogram ABCD, A = x + 30^o and D = x – 40^o, what is the measure of DCB?

Sol: In a parallelogram, sum of adjacent angles is equal to 180^o

 x + 30 + x – 40 = 180  x = 95^o

DAB

 = x + 30 = 95 + 30 = 125^o

 DCB = DAB = 125^o

(opposite angles of a parallelogram are equal)

11. In a circle of radius 49 cm, an arc subtends an angle of 36^o at the centre.

Find the length of the arc and the area of the sector.

Sol: Length of the arc = ^{2 r}₃₆₀^θ^{2 22 49 36} _{7 360}^{ }

 = 30.8 cm Area of the sector = ^r2 22 49 49 36

360 7 360

 θ   

 = 754.6 cm²

12. A rectangular plot of dimensions 13 m x 17 m is surrounded by a garden of width 5 m. What is the area (in sq m) the garden?

Sol: Let ABCD be the rectangular plot of given dimension. The shaded part is the surrounding garden. Now, the plot ABCD together with the garden forms another rectangular form PQRS. Dimensions of PQRS, as can be seen from the diagram, are:

Length PQ = width of garden + AB + width of garden

= 5 + 17 + 5 = 27 m

Similarly, breadth = PS = 5 + 13 + 5 = 23 m

Area of garden = Area of PQRS – Area of ABCD

= (27 x 23) – (17 x 13) = 621 – 221 = 440 sq m.

13. There is a rectangular field of length 100 m and breadth 40 m. A carpet of 2 m width is to be spread from the centre of each side to the opposite side.

What is the area of the carpet?

Sol: Area of the carpet ABCD = 40 m x 2 m = 80 m² Area of the carpet EFGH = 100 m x 2 m = 200 m² But the common area of two carpets = 2 x 2 = 4m²

So, area of the carpet = 200 + 80 – 4 = 276 m²

14. There is an equilateral triangle of which each side is 3 m. With all the three vertices as centres, circles with radius 1.5 cm are described (i) Calculate the area common to all the circles and the triangle. (ii) Find the area of the

remaining portion of the triangle.

Sol: (i) Area of each sector = ^{1 r2}

6  

So area common to the all the circles and triangle = 3 ^{1 r2 1 r2}

6 2

     

= ^{1 22 1.5 1.5}

2 7   = 3.53 m²

(ii) Area of the shaded portion = Area of the triangle – Area common to the triangle and the circles

But area of the triangle = ₄^3a2 ₄^{3(3)29 3}₄ m²

So area of the shaded portion = ^{9 3}₄ m² – 3.53 m² = 3.89 m² – 3.53 m² = 0.36 m²

Exercise:

1. The base and other side of an isosceles triangle is 10 cm and 13 cm respectively. Find its area.

1. 23 cm² 2. 60 cm² 3. 65 cm² 4. 23 cm²

2. If the area of triangle is 150 m² and base : height is 3 : 4, find its height and base respectively.

1. 75 m, 100 m 2. 100 m, 75 m 3. 75 m, 75 m 4. None

3. Find the area of an equilateral triangle of side of 12 cm.

1. 72 sq cm 2. 36 3 sq cm 3. 12 3sq cm 4. 18 3sq cm

4. The height of a triangle is 8/9^th of its base and its area is 576 sq cm. Find its height.

1. 36 cm 2. 52 cm 3. 72 cm 4. 32 cm

5. Find the area of a triangle whose sides are 66 cm, 88 cm and 1.1 m.

1. 2640 sq cm 2. 2904 sq cm 3. 2940 sq cm 4. 1452 sq cm

6. Area of an equilateral triangle is 16 3 sq cm, Find its perimeter.

1. 12 cm 2. 48 cm 3. 24 cm 4. 16 cm

7. What is the height of an equilateral triangle if its side is 8 3 cm?

1. 6 cm 2. 8 cm 3. 24 cm 4. 12 cm

8. In a quadrilateral, the length of its diagonals is 12 cm and the offsets drawn on this diagonal measure 13 cm and 7 cm respectively. Find its area.

1. 546 m² 2. 273 m² 3. 60 m² 4. 120 m²

9. In a parallelogram, the lengths of adjacent sides are 11 m and 13 m respectively. If the length of one diagonal is 16 m, find the length of other diagonal.

1. 18 m 2. 96 m 3. 18 m 4. 40 m

10. The two adjacent sides of a parallelogram are 12 m and 14 m respectively, and if the diagonal connecting the ends is 22 m respectively, find the area of the parallelogram.

1. 151.87 m² 2. 115.78 m² 3. 151.78 m² 4. 115.87 m²

11. The base and the height of a parallelogram are 25 cm and 20 cm respectively.

Find its area.

1. 500 sq cm 2. 250 sq cm 3. 45 sq cm 4. 125 sq cm

12. If the perimeter and diagonal of a rectangle and 14 cm and 5 cm respectively.

Find its area.

1. 6 cm² 2. 19 cm² 3. 12 cm² 4. 9 cm²

13. The area and the perimeter of a rectangle are 84 m² and 38 m respectively. Find its length and breadth.

1. 12 m, 7 m 2. 14 m, 6 m 3. 42 m, 19 m 4. None

14. A rectangular grass field is 112 m x 78 m. It has a gravel path 2.5 m wide all round it on the inside. Find the area of gravel path.

1. 8736 sq m 2. 925 sq m 3. 4368 sq m 4. 952 sq m

15. A rectangular lawn 70 m x 30 m has two roads each 5 m wide, running in the middle of it, one parallel to the length and the other parallel to the breadth.

Find the cost of gravelling the road at the rate of Rs.4 per sq m.

1. Rs.1000 2. Rs.2700 3. Rs.1700 4. Rs.2100

16. The length of a rectangle is increased by 20% and the breadth is decreased by 30%. Find the percentage change in its area.

1. 10% increase 2. 16% decrease

3. 8% decrease 4. 16% increase

17. The length and the breadth of a rectangle are in the ratio of 15 : 8 and its perimeter is 230 cm. Find its area.

1. 3000 sq cm 2. 2300 sq cm 3. 1500 sq cm 4. 6000 sq cm

18. There is a path of 1 m width around the outside of a rectangular field of 98 m x 48 m. Find the area of the path.

1. 148 sq m 2. 296 sq m 3. 598 sq m 4. 2352 sq m

19. The breadth of a rectangle is 4/5^th of its length and its area is 720 sq cm. Find its length.

1. 15 cm 2. 30 cm 3. 60 cm 4. 576 cm

20. The sides of a rectangle are in the ratio 4 : 3 and its area is 768 sq m. Find its perimeter?

1. 56 m 2. 112 m 3. 96 m 4. None

21. The perimeter of a rectangle is 216m. If its sides are in the ratio 5 : 4 the area is _______

1. 1140 sq m 2. 2880 sq m 3. 960 sq m 4. 1260 sq m

22. The sides of rectangular garden are 75 m x 48 m. What is the perimeter of a square with same area?

1. 60 m 2. 120 m 3. 240 m 4. None

23. Find the length of the diagonal of a square plot if its area is 900 sq m.

1. 10 ²m 2. 15 ²m 3. 30 ² m 4. 9 ²m

24. Find the perimeter of a square plot if its area is 1600 sq m.

1. 80 m 2. 160 m 3. 320 m 4. 40 m

25. Find the ratio of area and the perimeter of a square of side 8 cm.

1. 1 : 2 2. 4 : 1 3. 3 : 1 4. 2 : 1

26. Find the diagonal of a square whose perimeter is 128 ² sq m.

1. 64 m 2. 32 m 3. 32 ² m 4. 64 ² m

27. The perimeter of a square is 88 cm. Find its area.

1. 484 sq cm 2. 174 sq cm 3. 242 sq cm 4. None

28. There is a square shaped grass lane of 14 m side. Four cows are tethered with the ropes of 3.5 m length each at one corner. Find the area of the grass lane over which the cows are unable to graze the grass.

1. 157.5 sq m 2. 38.5 sq m 3. 175.5 sq m 4. 157.7 sq m

29. The area of two squares is in the ratio of 16 : 49. Find the ratio of their diagonals.

1. 7 : 4 2. 49 : 16 3. 4 : 7 4. None

30. If an error of 10% excess in made in calculating the side of square the % error in its area is ___________

1. 20 2. 21 3. 22 4. None

31. The area of a square garden is 576 sq m. What is the cost of fencing, it at the rate of Rs.1.25 per m?

1. Rs.24 2. Rs.50 3. Rs.90 4. None

32. The area of a square garden is 625 sq m. What is the area of a path of width 2.5 m around it, if the path is outside the garden?

1. 900 sq m 2. 275 sq m 3. 30 sq m 4. None

33. The diagonal of a square is 24 m. Its area is __________

1. 144 sq m 2. 576 sq m 3. 288 sq m 4. None

34. In a rhombus, the lengths of the two diagonals are 40 m and 30 m respectively.

Find its area and perimeter.

1. 600 sq m, 100 m 2. 100 sq m, 600 m

3. 1200 sq m, 600 m 4. 600 sq m, 200 m

35. In a rhombus the side and one of its diagonals are 25 m and 40 m respectively.

Find its perimeter.

1. 50 m 2. 100 m 3. 200 m 4. 10 m

36. The side and one of the diagonals of a rhombus are 25 cm and 14 cm respectively. Find its area.

1. 350 sq cm 2. 390 sq cm 3. 168 sq cm 4. 336 sq cm

37. The diagonals of a rhombus are in the ratio of 8 : 3 and area is 432 sq cm., Find its diagonals.

1. 18 : 48 2. 3 : 8 3. 48 : 18 4. None

38. If the side and the height of a rhombus are 12 m and 30 m respectively. Find the cost of painting both the surfaces of an aluminum sheet of same shape and size at the rate of Rs.5 per sq m.

1. Rs.1200 2. Rs.3600 3. Rs.3000 4. Rs.4200

39. The cross-section of a canal is a trapezium in shape. If the canal is 7 m wide at the top and 9 m at the bottom and the area of cross-section is 128 sq m, find the height of the canal.

1. 32 m 2. 8 m 3. 4 m 4. 16 m

40. The parallel sides of a trapezium are 18 cm and 22 cm and the distance between them is 10 cm. Find its area.

1. 100 sq cm 2. 250 sq cm 3. 200 sq cm 4. 150 sq cm

41. Find the area of a triangle having sides 3 m, 4 m and 5 m.

1. 60 sq m 2. 10 sq m 3. 12 sq m 4. 6 sq m

42. Find the area of a triangle whose base is 4.6m and height is 67 cm.

1. 154.10 sq m 2. 15410 sq m 3. 15.410 sq m 4. None

43. Find the area of an equilateral triangle each of whose sides measures 6 cm.

1. 36 sq cm 2. 3 3sq cm 3. 9 3sq cm 4. 12 sq cm

44. Length of the side of an equilateral triangle is

3

4 cm. Find its height.

1. 2 cm 2. 4 cm 3. 6 cm 4. None

45. Height of an equilateral triangle is 4 ³ cm. Find its area.

1. 4 3sq cm 2. 2 3sq cm 3. 16 3sq cm 4. 8 3sq cm

46. An isosceles right-angled triangle has two equal sides of length 6 m each. Find its area

1. 8 sq m 2. 36 sq m 3. 18 sq m 4. None

47. The perimeter of an isosceles triangle is 80 cm. If the length of the equal sides is given by 0.15 m, find the length of the base.

1. 40 m 2. 50 m 3. 12 m 4. 90.5 m

48. The perimeter of an isosceles triangle is 42 cm. If the base is 16 cm, find the length of equal sides.

1. 13 cm 2. 8 cm 3. 21 cm 4. 29 cm

49. The two adjacent sides of a parallelogram are 5 m and 6 m respectively, and if the diagonal connecting the ends is 9 m, find the area of the parallelogram (approximately).

1. 29 sq m 2. 28 sq m 3. 58 sq m 4. 50 sq m

50. Find the area of a quadrilateral of whose diagonal is 38 cm long and the lengths of perpendiculars from the other two vertices are 31 cm and 19 cm,

respectively.

1. 950 sq cm 2. 475 sq cm 3. 138 sq cm 4. 276 sq cm

51. Find the area of a parallelogram whose two adjacent sides are 130 m and 140 m and one of the diagonals is 150 m long.

1. 8400 sq cm 2. 16,800 sq cm 3. 2100 sq cm 4. None

52. Find the diagonal of a rectangle whose sides are 8 cm and 6 cm.

1. 14 cm 2. 5 cm 3. 20 cm 4. 10 cm

53. Find the perimeter of a rectangle of length 12 m and breadth 6 m.

1. 18 m 2. 72 m 3. 36 m 4. 144 m

54. Calculate the area of a rectangular field whose length is 12.5 cm and breadth is 8 cm.

1. 10 sq cm 2. 100 sq cm 3. 200 sq cm 4. 1 sq cm

55. Calculate the area of a rectangular field whose one side is 16 cm and the diagonal is 20 cm.

1. 192 sq cm 2. 96 sq cm 3. 294 sq cm 4. 72 sq cm

56. A rectangular carpet has an area of 120 sq m and perimeter of 46 m. Find the length of its diagonal.

1. 34 m 2. 51 m 3. 93 m 4. 17 m

57. The perimeter of a rectangle is 82 cm and its area is 400 sq m. Find the length of the rectangle.

1. 8 m 2. 16 m 3. 32 m 4. 64 m

58. If the area of a square field be 6050 sq m, find the length of its diagonal.

1. 220 m 2. 110 m 3. 55 m 4. None

59. Find the area of a square with perimeter 48 m.

1. 288 sq m 2. 72 sq m 3. 144 sq m 4. 96 sq m

60. Find the diagonal of a square field whose side is of 6 m length.

1. 12 ²m 2. 6 ²m 3. ²m 4. 3 ²m

61. Perimeter of a square field is 16 2cm. Find the length of its diagonal.

1. 16 cm 2. 4 cm 3. 8 cm 4. 64 cm

62. The area of a rhombus is 156 sq m. If one of its diagonals is 13 m, find the length of the other diagonal.

1. 12 m 2. 6 m 3. 48 m 4. 24 m

63. Find the area of a rhombus whose one side is 13 cm and one diagonal is 24 cm.

1. 60 sq cm 2. 120 sq cm 3. 240 sq cm 4. 74 sq cm

64. If the perimeter of a rhombus is 73 cm and one of its diagonals is 27.5 cm, find the other diagonal and the area of the rhombus.

1. 24 cm, 330 sq cm 2. 20 cm, 115 sq cm 3. 30 cm, 660.8 sq cm 4. 40 cm, 100.5 sq cm

65. In a rhombus, the lengths of two diagonals are 18 m and 24 m. Find its perimeter.

1. 15 m 2. 30 m 3. 60 m 4. 120 m

66. The diagonally of Rhombus are 12 cm and 5 cm respectively. Find the side of the Rhombus.

1. 5 cm 2. 6.5 cm 3. 6 cm 4. 8.5 cm

67. What is the radius of a circular plot whose circumference is 176 m?

1. 14 m 2. 56 m 3. 88 m 4. 28 m

68. A circular plot covers an area of 154 sq m. How much wire is required for fencing the plot?

1. 44 m 2. 22 m 3. 88 m 4. 77 m

69. Find the area of sector of a circle whose radius is 10 cm and the angle at the center is 36^o.

1. 30

7

3 sq cm 2. 31

3

7 sq cm 3. 30

3

7 sq cm 4. 31

7

3 sq cm

70. Find the area of sector of a circle whose radius is 12 cm and the length of the arc is 20 cm.

1. 60 sq cm 2. 240 sq cm 3. 120 sq cm 4. 64 sq cm

Cuboid :

A right prism with a rectangular base is called a Cuboid.

The sides of the base are length (l) and breadth (b). The height is h.

Lateral Surface Area = 2h(l + b)

Total Surface Area = 2h(l + b) + 2lb = 2(lb + bh + hl) Longest diagonal = ^l2^b2^h2

Volume = lbh

Cube:

If the length, breadth and height of a cuboid are all equal, it is called a cube.

Then, if edge of the cube = a Longest diagonal = 3a Lateral Surface Area = 6a² Total surface Area = 6a²

Volume = a³

Cylinder :

A cylinder can be considered to be a right prism except that instead of identical polygons a cylinder has identical circles for its top and

h l

b

a a a

r

h

base and it has a single lateral surface also called curved surface, instead of several rectangular surfaces.

The basic measurements are the radius of the base (or top) r and the height h.

Curved Surface (Lateral Surface Area) = 2πrh

Total surface Area = 2πrh+2πr² = 2πr(h + r) Volume = πr²h

Hollow Cylinder:

The cross section of a hollow cylinder is a ring.

Volume of the material of a hollow cylinder =

πh(R²-r²)

Here R is outer radius and r is inner radius of the hollow cylinder.

Cone:

A cone can be formed from the sector of a circle by rolling it and joining together its two straight edges. If r is the radius of the cone, and R is the radius of the sector of angle ^θ, then

1. r = R

360 θ 

2. Relation between r, l and h. (the radius, the slant height and height) is l² = h²+r²

3. Curved Surface area of Cone = prl

4. Total Surface Area = πrl + πr² = πr(l + r)

5. Volume =

3

1 πr²h

Sphere:

All points on the surface of a sphere are at the same distance from the center of the sphere. This distance is called the radius, r.

Surface Area of Sphere = 4πr² Volume of a Sphere =

3

4 πr³

The sphere has only one surface and hence only one surface area.

Hemisphere:

The radius is r.

r R

h

h

r

r

r

Curved Surface Area = 2πr²

Total Surface Area = 2πr²+πr² = 3πr² Volume =

3 r 2 3π 4 2

1 ₃ πr³

Examples:

1. A cuboid is 20 m x 10 m x 8 m. Find the length of diagonal, surface area and volume.

Sol: In a cuboid ,

Diagonal d = l²b²h² = 20²10²8² = 23.75 Surface are S = 2 (20 x 10 + 10 x 8 + 8 x 20) = 880 m² Volume = l x b x h = 20 x 10 x 8 = 1600 m³.

2. A cube has edge 12 m. Find its length of diagonal, surface area and volume.

Sol: In a cube

Diagonal d = Edge x 3 = 12 x 3 = 20.78 m Surface area S = 6 x (Edge)² = 6 x (12)² = 864 m² Volume V = Edge³ = (12)³ = 1728 m³.

3. The base of a right prism is a regular pentagon of side 18 cm. If the height of the prism is 2/3^rd of the side of the base, how much is the lateral surface area (in sq cm) of the prism?

Sol: Perimeter of the base of the prism

= number of sides x length of each side

= 5 x 18 = 90 cm.

Lateral surface area of a right prism = (Base perimeter) x (height)

= (90) ² 18 3

  

 

  = 1080 sq cm

4. If the radius of a sphere is increased by 50%, find the increase percent in volume and the increase percent in the surface area.

Sol: Let original radius = R. Then new radius = ^{150R 3R}

100  2 . Original volume = ^{4 R3}

3 , New volume ^{4 3R 3} 9 R³

3 2

 

    . Increase % in volume = ^{19 R3 3} ₃ ¹⁰⁰

6 4 R

    

 



 % = 237.5%

Original surface area = 4R². New surface area = 4 ^{3R 2} 9 R² 2

 

    . Increase % in surface area = ^{5 R2}₂ ¹⁰⁰

4 R

  

  

  

 % = 125%.

5. A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. Find the radius of the cone?

Sol: Let the radius of the cone be r cm.

Then, ¹ r² 6 8 8 2 r^{2 8 8 2 3}

3 6

  

 

            

  = 64  r = 8 cm.

6. A brick measures 10 cm x 5 cm x 3 cm. How many bricks will be required for a wall of 100 metre long 6 metre high and 1.5 metre thick?

Sol: Volume of the wall = 100 m x 6 m x 1.5 m = 900 m³ Volume of one brick = ^{1 m 1 m 3 m 3 m3}

10 20 100 20000

 No. of bricks required = ^900m3

3 = 60,00,000

3

20000m³

7. What is the maximum length of a pencil which can be inscribed in a box of length 24 units, breadth 3 units and height 4 units?

Sol: Maximum length in a cuboid is its diagonal

 Length of main diagonal is ^{length2breadth2height2}

=      ^{242 32 22 576 9 4   589 units}

8. The height and base-radius of a right circular cone are 10 cm and 24 cm

respectively. What is the area of the curved surface area (in sq cm) if the cone?

Sol: Curved surface area of a cone = ^rl, R and l being radius and slant height.

It is given that height h = 10 cm and radius = 24 cm.

L2 = h2 + r2 = 102 +242

 l = 26 (10 and 24 are in the ratio of 5 : 12; hence l will be the 2 x 13 = 26 Hence, curved surface area = ^rl = ^ x 24 x 26 624^ sq cm.

Exercise:

1. The surface area of cube is 96 sq cm. Find its volume.

1. 48 cm³ 2. 64 cm³ 3. 16 cm³ 4. 32 cm³

2. The volume of a cube is 125 cm³. Find its surface area.

1. 25 cm² 2. 375 cm² 3. 150 cm² 4. 250 cm²

3. The diagonal of a cube is 3 cm. Find its surface area.

1. 12 cm² 2. 102 cm² 3. 18 cm² 4. 36 cm²

4. A cube of 6 cm side melted and smaller cubes of 2 cm side are manufactured.

Find the number of smaller cubes so formed.

1. 12 2. 27 3. 24 4. 8

5. Two cubes have their volumes in the ratio 8 : 27. The ratio of their surface areas is ___________

1. 2 : 3 2. 9 : 4 3. 2 : 9 4. 4 : 9

6. A cube of side 6 cm is cut into a number of cubes, each of side 3 cm. Find the number of cubes.

1. 8 2. 9 3. 24 4. 5

7. The percentage increase in the surface area of a cube when each side is doubled is ______________

1. 100% 2. 200% 3. 300% 4. 400%

8. How many bullets can be made out of a cube of lead whose edge measures 22 cm each bullet being 2 cm in diameter?

1. 5324 2. 2662 3. 1347 4. 2541

9. The maximum length of a pencil which can be accommodated in a cubical box of 10 cm side.

1. 10 3cm 2. 5 3cm 3. 20 3cm 4. 100 3cm

10. The length, breadth & height of a cuboid are in the ratio of 4 : 3 : 2 and its volume is 3000 m³. Find its surface area.

1. 1300 m² 2. 1500 m² 3. 1333 m² 4. 27000 m²

11. Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is ___________

1. 360 cm² 2. 36 cm² 3. 216 cm² 4. 360 m²

12. Find the area of the four walls of a room of 6 m x 4 m x 3 m.

1. 120 m³ 2. 84 m³ 3. 42 m³ 4. 60 m³

13. The dimensions of a room are 200 m x 15 m x 10 m. What is the cost of painting its four walls at the rate of Rs.15 per 100 sq m?

1. Rs.70 2. Rs.105 3. Rs.225 4. None

14. The dimensions of a room are 16 m x 10 m. There are 2 doors 5 m x 4 m and 4 windows 5 m x 2.5 m. What is the cost of painting the wall and the top at the cost of Rs.1.50 per 10 sq m?

1. Rs.96 3 Rs.112.5 3. Rs.126 4. None

15. A well with 14 m inside diameter is dug 10 m deep. Earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment.

The height of the embankment is ____

1. 2

1 m 2.

3

2 m 3.

4

3 m 4.

5 3m

16. The radius and height of a cylinder are 6 cm & 14 cm respectively. Find the ratio of its curved surface area and volume.

1. 1584 : 528 2. 36 : 196 3. 528 : 1584 4. None

17. The radius and height of a cylinder are in the ratio of 2 : 1 and its volume is 616 cubic cm. Find its curved surface area.

1. 1848 cm² 2. 627 cm² 3. 612 cm² 4. 672 cm²

18. The radii of two cylinders are in the ratio 2 : 3 and the heights are in the ratio of 3 : 4. Find the ratio of their volumes.

1. 4 : 3 2. 3 : 1 3. 1 : 3 4. 6 : 12

19. A cylinder of radius 2 cm is melted and 11 cubes of 2 cm side are manufactured. Find the height of the cylinder melted.

19. A cylinder of radius 2 cm is melted and 11 cubes of 2 cm side are manufactured. Find the height of the cylinder melted.

In document 208666617 Total Book Rough (Page 67-83)