A rectangular tank, 70 cm by 55 cm by 40 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 5 : 4. If
57 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 55 x 9
= 34650 cm
3 5 u = 34650 cm
3 1 u = 34650 ÷ 5 = 6930 cm
3 4 u = 4 x 6930 = 27720 cm
3 Volume of water in
57 of the barrel = 27720 cm
3 Volume of the barrel
= 27720 ÷
57 = 27720 x
75 = 38808 cm
3 (b)
Volume of the tank
= 70 x 55 x 40
= 154000 cm
3 Number of barrels to fill the tank
= 154000 ÷ 38808
= 3 r 37576
Minimum number of barrels to fill the tank
= 3 + 1
= 4
Answer(s): (a) 38808 cm
3; (b) 4