Question

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are $5cm$ and $13cm$ respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is $30cm$.

Answer 1

Height of the cylindrical part $=13$cm

Radius of cone , cylinder and hemi sphere$=5$cm

r=5cm for hemisphere cylinder and cone.

Height of cone $h=$$30-5-13=12$

The area of canvas required=Surface area of hemishphere,cylinder and cone parts of tent

$A=2\pi r^2+2\pi rH+\pi r\left(\sqrt{h^2+r^2}\right)$

$A=2\pi \times 5\times 5+2\pi \times 5\times 13+\pi \times 5\left(\sqrt{5^2+{12}^2}\right)$

$A=770c{m}^2$