A rectangular tank, 90 cm by 55 cm by 50 cm, is filled with water to a height of 9 cm. The ratio of the volume of water in the tank to that in a barrel is 11 : 6. If
23 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
= 90 x 55 x 9
= 44550 cm
3 11 u = 44550 cm
3 1 u = 44550 ÷ 11 = 4050 cm
3 6 u = 6 x 4050 = 24300 cm
3 Volume of water in
23 of the barrel = 24300 cm
3 Volume of the barrel
= 24300 ÷
23 = 24300 x
32 = 36450 cm
3 (b)
Volume of the tank
= 90 x 55 x 50
= 247500 cm
3 Number of barrels to fill the tank
= 247500 ÷ 36450
= 6 r 28800
Minimum number of barrels to fill the tank
= 6 + 1
= 7
Answer(s): (a) 36450 cm
3; (b) 7