A rectangular tank, 80 cm by 40 cm by 40 cm, is filled with water to a height of 10 cm. The ratio of the volume of water in the tank to that in a barrel is 5 : 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 tank.
(a)
Volume of water in the tank
= 80 x 40 x 10
= 32000 cm
3 5 u = 32000 cm
3 1 u = 32000 ÷ 5 = 6400 cm
3 2 u = 2 x 6400 = 12800 cm
3 Volume of water in
23 of the barrel = 12800 cm
3 Volume of the barrel
= 12800 ÷
23 = 12800 x
32 = 19200 cm
3 (b)
Volume of the tank
= 80 x 40 x 40
= 128000 cm
3 Number of barrels to fill the tank
= 128000 ÷ 19200
= 6 r 12800
Minimum number of barrels to fill the tank
= 6 + 1
= 7
Answer(s): (a) 19200 cm
3; (b) 7