5Dec19 FS Q36

0. A solid is in the form of a cylinder with hemispherical ends. The diameter of the cylinder is 1/3 of its height (excluding the hemispherical ends). The total length of the solid including the hemispherical ends is 56 cm. What is the surface area of the solid?

Answer
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Option : B
Explanation :
Let ADCDEF is a cylinder with hemispherical ends.

Diameter of the cylinder BD = 2d
height of the cylinder AD = 6d
total length = 6d + d + d = 56
8d=56
d=7cm.
Surface area of the solid
= Surface area of cylindrical parts + 2 x surface area of hemisphere
= 2π x d x 6d + 2 x 2π (d)²
= 12πd² + 4πd² = 16πd²
= 16 x (22/7) x 7² = 2464 cm²

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