A water tank is in the shape of a cuboid. The edges of the tank are in the ratio 7 ∶ 5 ∶ 3. The surface area of the tank is 142 m2, find how many liters of water the tank can hold?
1. 105 kL
2. 110 kL
3. 102 kL
4. 108 kL
1. 105 kL
2. 110 kL
3. 102 kL
4. 108 kL
Correct Answer – Option 1 : 105 kL
Given:
Ratio of sides = 7 ∶ 5 ∶ 3
Total surface area of the tank = 142 m2
Formula used:
Total surface area of the cuboid = 2(lb + bh + hl)
Volume of cuboid = l × b × h
1m3 = 1000 liters
Calculation:
Let the sides of the tank = 7x, 5x and 3x
∵ TSA of the tank = 2(lb + bh + hl)
⇒ 142 = 2[(7x × 5x) + (5x × 3x) + (3x × 7x)]
⇒ 142 = 2(35x2 + 15x2 + 21x2)
⇒ 142 = 2(71x2)
⇒ 71 = 71x2
⇒ x = √1 = 1 ——(Ignore the negative value)
∴ Sides of the tank are;
7x = 7 × 1 = 7m
5x = 5 × 1 = 5m
3x = 3 × 1 = 3m
∴ Volume of the tank in m3 = (7 × 5 × 3) m3 = 105 m3
∵ 1 m3 = 1000 liters
∴ 105 m3 = (1000 × 105) = 105000 liters = 105 kiloliters
∴ Tank can hold 105 kiloliters of water.