A rectangular container, 90 cm by 45 cm by 45 cm, is filled with water to a height of 12 cm. The ratio of the volume of water in the container to that in a barrel is 9 : 2. If
23 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 45 x 12
= 48600 cm
3 9 u = 48600 cm
3 1 u = 48600 ÷ 9 = 5400 cm
3 2 u = 2 x 5400 = 10800 cm
3 Volume of water in
23 of the barrel = 10800 cm
3 Volume of the barrel
= 10800 ÷
23 = 10800 x
32 = 16200 cm
3 (b)
Volume of the container
= 90 x 45 x 45
= 182250 cm
3 Number of barrels to fill the container
= 182250 ÷ 16200
= 11 r 4050
Minimum number of barrels to fill the container
= 11 + 1
= 12
Answer(s): (a) 16200 cm
3; (b) 12