Question

A cone is made of a sector with a radius of 14 cm and and angle of ${60}^{\circ }$. What is total suface area of the cone?

• A. $119.78c{m}^2$
• B. $191.87c{m}^2$
• C. $196.5c{m}^2$
• D. None of these

Answer 1

The correct option is A $119.78c{m}^2$

Let the radius of cone be R and radius of sector =r,

then the slant height of cone (l) =r
and $2\pi R=2\pi r\times \frac{60}{360}$
$\Rightarrow R=\frac{r}{6}=\frac{14}{6}=\frac{7}{3}cm$
$\therefore$ Total surface area $=\pi r(l+r)$
$=\frac{22}{7}\times \frac{7}{3}(14+\frac{7}{3})$
$=119.78c{m}^2$