Question

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7m and height of the cone is 1m, what is the area of cloth required? ($\sqrt{2}=1.414$)

• A. 262.39 m²
• B. 463.39 m²
• C. 662.39 m²
• D. 563 m²

Answer 1

The correct option is B

463.39 m²

Area of the cloth required = C.S.A of Hemisphere + C.S.A of cone

Area of the cloth required = $2\pi r^2+\pi rl$....(i)

For calculating the surface area of a cone we need to calculate its slant height,

l = $\sqrt{49+1}=\sqrt{50}$ m = $\sqrt{25\times 2}=5\sqrt{2}$ m.

Substituting the values in equation (i)

Area of the cloth required = $\pi r(2r+l)$
= $\frac{22}{7}\times 7(14+5\sqrt{2})$
= $22(14+7.05)$
= $22\times 21.05$
= $463.1m^2$