Page 291 - Start Up Mathematics_8 (Non CCE)

fi 2h × (17.5) = 105 fi 35h = 105

105
fi h = = 3 m
35
\ Volume of room = l × b × h = 13 m × 4.5 m × 3 m = 175.5 m 3

EXERCISE 18.2

1. Find the total surface area and lateral surface area of a cuboid with length = 3.5 m, breadth = 32 dm
and height = 260 cm.
2. Find the length of the diagonal of a cuboid with length = 10 cm, breadth = 8 cm and height = 4 cm.
3. Find the total surface area, lateral surface area and the length of the diagonal of a cube whose edge is:
(a) 4.5 cm (b) 3.2 m (c) 12 dm (d) 1 dm 5 cm
4. Find the surface area of a cube whose volume is:
3
3
3
(a) 512 m (b) 64 dm (c) 125 cm (d) 216 m 3
5. Find the volume of a cube whose surface area is:
2
2
2
(a) 54 cm (b) 294 m (c) 384 dm (d) 486 cm 2
6. Three cubes of edges 8 cm are joined end to end. Find the surface area of the resulting cuboid.
7. Find the cost of painting 3 iron boxes at the rate of ` 5 per square metre, whose dimensions are
1.5 m × 0.85 m × 0.20 m, 2 m × 0.65 m × 0.35 m and 2 m × 0.90 m × 0.45 m.
8. The ratio of the surface areas of two cubes is 16 : 25. Find the ratio of their volumes.
9. The perimeter of a floor of a rectangular hall is 60 m and its height is 3 m. Find the cost of painting
2
its four walls at the rate of ` 20 per m .
2
2
10. A cuboid has total surface area of 60 m and lateral surface area of 40 m . Find the area of its base.
11. The length of a hall is 22 m and width is 18 m. The sum of the areas of the floor and the flat roof is
equal to the sum of the area of the four walls. Find the height and volume of the hall.
12. A solid cube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the
given cube and that of one of the cuboids.
13. The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost
2
of covering it with a cloth at the rate of ` 10 and ` 11 per m is ` 1,300. Find the dimensions of the
box.
14. A rectangular swimming pool 30 m long, 20 m wide and 1.5 m deep is to be tiled. If each tile is
50 cm × 50 cm, how many tiles will be required?
15. A log of wood of dimensions 2 m × 20 cm × 10 cm is cut into small blocks of 10 cm × 5 cm × 4 cm.
How many blocks do we get? What will be the total surface area of all these blocks?
16. The dimensions of a building are 30 m × 20 m × 40 m. If the walls, floor and roof of this building
are to be repaired, the contractor asks for ` 50 per square metre. What will be the estimate of the
contractor for this work?

Cylinder
Let’s consider objects like a gas cylinder, coke cans, etc. These solids have a B
curved lateral surface with congruent circular ends. Such solids are right circular
cylinders. A right circular cylinder has two plane ends, also called base of the cylinder Axis
(Fig. 18.3). The two bases are circular in shape and parallel to each other.
Axis: The line segment joining the centres of the two bases is called the axis of the cylinder. A
In Fig. 18.3, AB is the axis of the cylinder. The axis of the cylinder is perpendicular to Fig. 18.3
the circular ends.

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