A rectangular tank, 90 cm by 50 cm by 50 cm, is filled with water to a height of 12 cm. The ratio of the volume of water in the tank to that in a barrel is 9 : 4. If
34 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 50 x 12
= 54000 cm
3 9 u = 54000 cm
3 1 u = 54000 ÷ 9 = 6000 cm
3 4 u = 4 x 6000 = 24000 cm
3 Volume of water in
34 of the barrel = 24000 cm
3 Volume of the barrel
= 24000 ÷
34 = 24000 x
43 = 32000 cm
3 (b)
Volume of the tank
= 90 x 50 x 50
= 225000 cm
3 Number of barrels to fill the tank
= 225000 ÷ 32000
= 7 r 1000
Minimum number of barrels to fill the tank
= 7 + 1
= 8
Answer(s): (a) 32000 cm
3; (b) 8