A water tank is in the shape of a cuboid. The edges of the tank are in

1.	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 kL2. 110 kL3. 102 kL4. 108 kL
Answer» 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.

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 kL2. 110 kL3. 102 kL4. 108 kL

Answer» 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.