A rectangular tank, 70 cm by 45 cm by 40 cm, is filled with water to a height of 11 cm. The ratio of the volume of water in the tank to that in a barrel is 7 : 6. If
35 of the barrel is filled with water, find
- the volume of the barrel.
- the minimum number of such barrels to fill the tank.
(a)
Volume of water in the tank
= 70 x 45 x 11
= 34650 cm
3 7 u = 34650 cm
3 1 u = 34650 ÷ 7 = 4950 cm
3 6 u = 6 x 4950 = 29700 cm
3 Volume of water in
35 of the barrel = 29700 cm
3 Volume of the barrel
= 29700 ÷
35 = 29700 x
53 = 49500 cm
3 (b)
Volume of the tank
= 70 x 45 x 40
= 126000 cm
3 Number of barrels to fill the tank
= 126000 ÷ 49500
= 2 r 27000
Minimum number of barrels to fill the tank
= 2 + 1
= 3
Answer(s): (a) 49500 cm
3; (b) 3