Question

A wooden toy is in the shape of a cone mounted on a cylinder as shown in the figure. If the height of the cone is $24cm$, the total height of the toy is $60cm$ and the radius of the base of the cone is equal to $10cm$ and is twice the radius of the base of the cylinder. Find the total surface area of the toy. [Take $\pi =3.14$]

Answer 1

Given:

Height of cylinder, $h$= Total height of toy - Height of cone $=60-24$$=36cm$

Radius of cone, $r=10cm$

Slant height, $l=\sqrt{{10}^2+{24}^2}$$=26cm$

Surface Area of cone $=\pi r^2+\pi rl$$=\pi ({10}^2+10\times 26){cm}^2$

$=360\pi {cm}^2$

According to given condition in the question:

Radius of cylinder$R=5cm\dots (\frac{10}{2}=R)$ or $(r=2R)$

Surface Area of cylinder$=\pi r^2+2\pi rh$$=\pi (5^2+2\times 5\times 36){cm}^2$

$=385\pi {cm}^2$

Total Surface area of the toy$=(360+385)\pi {cm}^2$

$=2340.5{cm}^2$