Question

A toy is in the form of a cone mounted on a hemisphere of common base radius $7$ cm. The total height of the toy is $31$ cm. Find the total surface area of the toy.

Answer 1

Since total height of toy is $31$cm,

So, the height of cone is $\left(h\right)=31-7=24$cm

Also,radius of cone$\left(r\right)=7$cm

Now, $l=\sqrt{7^2+{24}^2}=\sqrt{49+576}=\sqrt{625}=25$cm

Now, total surface area of toy$=2\pi r^2+\pi rl=\pi r(2r+l)$

$=\frac{22}{7}\times 7(14+25){cm}^2$

$=22\times 39=858$sq.cm

Hence total surface area is $858$ sq.cm