Mathematics

The horizontal cross-section of a water tank is in the shape of a rectangle with semi-circle at one end, as shown in the following figure. The water is 2.4 meters deep in the tank. Calculate the volume of water in the tank in gallons.
Given : 1 gallon = 4.5 litres

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Let radius of semi-circle be r meters.

From figure,

⇒ 2r = 7 m

⇒ r = 3.5 m

The semi-circle cross section of water tank can be considered as a half-cylinder.

Volume of water in water tank = Volume of rectangular side + Volume of semi-circle side

= lbh + $\dfrac{πr^2h}{2}$

= 21 × 7 × 2.4 + $\dfrac{1}{2} \times \dfrac{22}{7} \times 3.5^2 \times 2.4$

= 352.8 + 46.2

= 399 m³.

= 399 × (100)³ cm³

= 399 × 1000000 cm³

Since, 1 liter = 1000 cm³.

= 399 × 1000000 × $\dfrac{1}{1000}$ litre

= 399000 litre.

Since, 1 gallon = 4.5 litres

= 399000 $\times \dfrac{1}{4.5}$ gallons

= 88666.67 gallons.

Hence, volume of water in tank = 88666.67 gallons.

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