Question

A toy is in the form of cone of radius $3$ cm and height $4$ cm mounted on a hemisphere of same radius, then find the T. S. A (Total Surface Area) of the toy.

Answer 1

Taking both the cone and the hemi-sphere be hollow.

Given the radius of cone $\left(r\right)=3$ cm and height $\left(h\right)=9$ cm.

Then the slant height of the cone be $\left(l\right)=\sqrt{r^2+h^2}=\sqrt{3^2+4^2}=5$ cm.

Now surface of the cone $\left(S_1\right)=\pi rl=15\pi$ cm${}^2$.

Also given the radius of the hemi-sphere being $=3$ cm.

Now the surface area of the hemi-sphere being $\left(S_2\right)=\frac{2}{3}\pi 3^2=6\pi$ cm${}^2$.

$\therefore$ total surface are of the toy $=S_1+S_2=21\pi$ cm${}^2$.