A rectangular container, 90 cm by 45 cm by 45 cm, is filled with water to a height of 11 cm. The ratio of the volume of water in the container to that in a barrel is 9 : 4. If
25 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 11
= 44550 cm
3 9 u = 44550 cm
3 1 u = 44550 ÷ 9 = 4950 cm
3 4 u = 4 x 4950 = 19800 cm
3 Volume of water in
25 of the barrel = 19800 cm
3 Volume of the barrel
= 19800 ÷
25 = 19800 x
52 = 49500 cm
3 (b)
Volume of the container
= 90 x 45 x 45
= 182250 cm
3 Number of barrels to fill the container
= 182250 ÷ 49500
= 3 r 33750
Minimum number of barrels to fill the container
= 3 + 1
= 4
Answer(s): (a) 49500 cm
3; (b) 4