Page 287 - Start Up Mathematics_8 (Non CCE)

Width of box (b) = {48 – (5 + 5)} = (48 – 10) cm = 38 cm
Height of box (h) = 5 cm

\ Volume of box = l × b × h = 42 cm × 38 cm × 5 cm = 7,980 cm 3

EXERCISE 18.1

1. Find the volume of a cuboid whose dimensions are:
(a) length = 15 cm, width = 12 cm and height = 8 cm
(b) length = 4 m, width = 2.6 m and height = 80 cm
2. Find the volume of a cube whose side is: (a) 6.3 cm (b) 7.2 dm (c) 5 m
3. A water tank is 1.5 m long, 1.3 m wide and 0.5 m deep. How many litres of water can it hold?
4. What will happen to the volume of a cube, if each of its edges is halved?
5. A swimming pool is 200 m long and 120 m wide. 36 litres of water is pumped into it. Find the rise
in level of water.
6. A cuboid has dimensions 25 dm × 15 dm × 8 dm. How much does its volume differ from that of a
cube with an edge of 16 dm?
7. The dimensions of a cistern are 2 m 75 cm × 1 m 90 cm × 1 m 40 cm. How many litres of water can
this cistern hold if we fill it till the top?
3
8. A volume of a cuboidal box is 250 cm . If its length is 20 cm and height is 5 cm, find its breadth.
9. How many cubes of edge 0.5 cm are required to make a cube of side 3 cm?
10. A cuboidal shape gold biscuit is of dimensions 8 cm × 5 cm × 2 cm. From this gold biscuit, small
3
lockets each of volume 2.5 cm are made. How many such lockets can be made from this gold biscuit?
11. Two cubes are such that the length of the side of cube I is twice the length of the side of cube II.
Find the ratio of the volume of cube I to that of cube II.
1 3
12. How many alarm clocks of size 5 cm × 10 cm × 10 cm can be packed into a box of size 1 m × m × m?
2 4
13. Three cubes having edges 18 cm, 24 cm and 30 cm respectively are melted and made into a new
cube. Find the edge of the new cube so formed.
14. The outer dimensions of a jewellery box made of wood are 20 cm × 16 cm × 8 cm. The thickness
3
of the wood is 1 cm. Find the total cost of wood required to make the box, if 1 cm of wood costs
` 2.50.
15. An aluminium sheet is of dimension 38 cm × 38 cm. From each of its corners, a square of 4 cm is
cut. An open box is made of the remaining sheet. Find the volume of the box.
16. A locality in Delhi having a population of 1,200 requires 150 L water per head, per day. It has a big
tank measuring 30 m × 25 m × 10 m. For how many days will the water of this tank last?

Surface Area of a Cuboid and Cube
(a) Surface area of a cuboid: A cuboid consists of 6 rectangular faces. So, its surface area is equal to the
sum of the areas of its 6 rectangular faces. G
Let there be a cuboid of length l cm, breadth b cm and l F
height h cm (Fig. 18.2). A B
(i) Area of face ABFG = Area of face DCEH = l × b cm 2
(ii) Area of face ADHG = Area of face BCEF = b × h cm 2 b H E

(iii) Area of face ABCD = Area of face HEFG = l × h cm 2 D l C
Fig. 18.2
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