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 7 m and height of the cone is 1 m, what is the area of cloth required? $(\sqrt{2}=1.414)$

• A. 563 $m^2$
• B. 262.39 $m^2$
• C. 463.1 $m^2$
• D. 662.39 $m^2$

Answer 1

The correct option is C 463.1 $m^2$

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