Question

The circumference of the base of a $16$m high solid cone is $33$m. Find the surface area of the cone.

Answer 1

The circumference of the base of a cone is $33m$.

$\therefore 2\pi r=33$

$\Rightarrow \frac{22}{7}\times 2\times r=33$

$\Rightarrow r=\frac{33\times 7}{22\times 2}=\frac{3\times 7}{4}=\frac{21}{4}=5.25m$

Now, the height of the cone is $16m$.

$\therefore$ The slant height $l$ of the cone is $l=\sqrt{h^2+r^2}=\sqrt{{16}^2+(5.25{)}^2}=16.84m$

$\therefore$ The surface area is $\pi \times r\times l=277.85m^2$