A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is 1/4 of its height. The surface area of the solid is :

Answer: Option D

Let the radius of the cylinder and the hemisphere be r cm
Diameter of the cylinder = (2r) cm
Height of the cylinder = (4 × 2r) cm = 8r cm
Total length of the solid :
= (8r + r + r) cm = 10r cm
⇒ 10r = 35
⇒ r = 3.5

∴ Surface area of the solid :
= Curved surface area of the cylinder + 2 × (Curved surface area of the hemisphere)
$$=\left(2\times \frac{22}{7}\times 3.5\times 28+2\times 2\times \frac{22}{7}\times 3.5\times 3.5\right)\text{ c}{\text{m}}^2$$
$$\begin{array}{rl}& =\left(616+154\right)\text{ c}{\text{m}}^2\\ & =770\text{ c}{\text{m}}^2\end{array}$$