Question

A toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone is $6cm$ and its height is $4cm$. Find the surface area of the toy. $(\pi =3.14)$

Answer 1

Diameter of the base of toy (cone)
$d=6cm$
Radius of the base of the cone, $r=\frac{6}{2}=3cm$
Height of the cone, $h=4cm$
Slant height of the cone, $l=\sqrt{r^2+h^2}$
$=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5cm$
Curved surface area of the cone $=\pi rl$
$=\frac{22}{7}\times 3\times 5=\frac{330}{7}c{m}^2$
Radius of the hemisphere $=3cm$
Curved surface area of the hemisphere
$=2\pi r^2=2\times \frac{22}{7}\times 3\times 3=\frac{396}{7}$
The surface area of the toy = curved
surface area of cone+curved surface area of the hemisphere
$=\frac{330}{7}+\frac{396}{7}=\frac{726}{7}=103.71c{m}^2$