A rectangular tank, 70 cm by 45 cm by 50 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 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 10
= 31500 cm
3 7 u = 31500 cm
3 1 u = 31500 ÷ 7 = 4500 cm
3 6 u = 6 x 4500 = 27000 cm
3 Volume of water in
35 of the barrel = 27000 cm
3 Volume of the barrel
= 27000 ÷
35 = 27000 x
53 = 45000 cm
3 (b)
Volume of the tank
= 70 x 45 x 50
= 157500 cm
3 Number of barrels to fill the tank
= 157500 ÷ 45000
= 3 r 22500
Minimum number of barrels to fill the tank
= 3 + 1
= 4
Answer(s): (a) 45000 cm
3; (b) 4