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?

• A. 262.39 $m^2$
• B. 463.39 $m^2$
• C. 662.39 $m^2$
• D. 563 $m^2$

Answer 1

The correct option is B

463.39 $m^2$

Given

r = 7m
h = 1m

Surface area of hemisphere = 2$\pi$$r^2$
$=2\times \frac{22}{7}\times (7{)}^2$ = 308 $m^2$.

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

l = $\sqrt{r^2+h^2}$

l = $\sqrt{49+1}=\sqrt{50}$ m.

Surface area of cone = $\pi$rl= $\frac{22}{7}\times 7\times \sqrt{50}=155.39m^2$.

So, area of cloth required = (308 + 155.39)$m^2$ = 463.39 $m^2$