Mathematics

Shown alongside is a horizontal water tank composed of a cylinder and two hemispheres. The tank is filled up to a height of 7 m. Find the surface area of the tank in contact with water. Use $\pi = \dfrac{22}{7}$ .

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From figure,

Radius of cylindrical part = Radius of hemispherical part = r = 7 m.

Length (Height h) of the cylindrical part = 34 - 7 - 7 = 20 m.

Surface of cylindrical part in contact of water

= $\dfrac{1}{2} \times 2πrh = \dfrac{1}{2} \times 2 \times \dfrac{22}{7} \times 7 \times 20$ = 440 m²

Surface of each hemisphere in contact of water

= $\dfrac{1}{2} \times 2πr^2$

= πr²

= $\dfrac{22}{7} \times 7^2$

= 22 × 7

= 154 m².

∴ Surface area of the tank in contact of water = 440 + 2 × 154

= 440 + 308

= 748 m².

Hence, surface area of tank in contact with water = 748 m².

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