A cubical water tank can hold $125$ liters of water. What will the cost of painting its outer walls be at $$ 10$ per square centimeter?

$ 50, 000

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$ 75, 000

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$ 100, 000

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$ 200, 000

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Solution

The correct option is C $$ 100, 000$
Amount of water the tank can hold = volume of the tank
$1 L = 1000 c u c m$
$\Rightarrow 125 L = 125 \times 1000 = 125000 c u c m$
Volume of the tank $= s^{3} = 125000 c m^{3}$ , where $s$ is the side length of the tank
$\Rightarrow s = \sqrt[3]{125000} = 50 c m$

The outer walls of the tank need to be painted, i.e., the lateral surface area of the tank needs to be painted.
Lateral surface area of the tank $= 4 \times s^{2} = 4 \times 50^{2} = 4 \times 2500$
$= 10000 s q c m$

Painting cost $= $ 10 p e r s q c m$
Cost of painting the walls of the tank $= 10 \times 10000 = $ 100, 000$

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A cubical water tank can hold 125 liters of water. What will the cost of painting its outer walls be at $10 per square centimeter?

A cubical water tank can hold $125$ liters of water. What will the cost of painting its outer walls be at $$ 10$ per square centimeter?