Question

A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are $5cm$ and $4cm$ respectively. Determine the surface area of the toy?

Answer 1

The height of the cone is 4 cm and the diameter of the cone is 5 cm, so the radius of the cone will be $\frac{5}{2}cm$.

The slant height of the cone is,

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

$=\sqrt{{\left(\frac{5}{2}\right)}^2+{\left(4\right)}^2}$

$=\sqrt{\frac{25}{4}+16}$

$=\sqrt{\frac{89}{4}}$

$=4.7$

The surface area of the cone is,

$A=\pi rl$

$=\frac{22}{7}\times \frac{5}{2}\times 4.7$

$=36.9c{m}^2$

Now, the diameter of the hemisphere is 5 cm, then the radius of the hemisphere will be $\frac{5}{2}cm$.

The surface area of the hemisphere will be,

$A=2\pi r^2$

$=2\times \frac{22}{7}\times \frac{5}{2}\times \frac{5}{2}$

$=39.2c{m}^2$

The total surface area of the toy is,

$A=36.9+39.2$

$=76.1c{m}^2$

Therefore, the total surface area of the toy is $76.1c{m}^2$.