A rectangular container, 90 cm by 50 cm by 50 cm, is filled with water to a height of 5 cm. The ratio of the volume of water in the container to that in a barrel is 9 : 2. If
57 of the barrel is filled with water, find
- the volume of the barrel.
- the minimum number of such barrels to fill the container.
(a)
Volume of water in the container
= 90 x 50 x 5
= 22500 cm
3 9 u = 22500 cm
3 1 u = 22500 ÷ 9 = 2500 cm
3 2 u = 2 x 2500 = 5000 cm
3 Volume of water in
57 of the barrel = 5000 cm
3 Volume of the barrel
= 5000 ÷
57 = 5000 x
75 = 7000 cm
3 (b)
Volume of the container
= 90 x 50 x 50
= 225000 cm
3 Number of barrels to fill the container
= 225000 ÷ 7000
= 32 r 1000
Minimum number of barrels to fill the container
= 32 + 1
= 33
Answer(s): (a) 7000 cm
3; (b) 33