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 5 cm and 13 cm respectively. The radii of the hemispherical and the 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 30 cm.

Answer 1

The radius of the hemisphere = 5 cm

The radius of the base of cylinder = 5 cm

The radius of the base of the cone = 5 cm

Height of hemisphere = its radius = 5 cm

Let the height of cone = h

Then $(5+13+h)=30\Rightarrow h=30-18=12$ cm

Slant height of the cone, $l=\sqrt{r^2+h^2}=\sqrt{5^2+{12}^2}=\sqrt{25+144}=\sqrt{169}=13cm$

The surface area of the toy = Curved surface area of the hemisphere + Curved surface area of cylinder + Curved surface area of the cone

$=2\pi r^2+2\pi rh+\pi rl=2\pi \times 5^2+2\pi \times 5\times 13+\pi \times 5\times 13=245\pi c{m}^2=245\times \frac{22}{7}=770c{m}^2$

Hence, the surface surface area of the toy is 770 sq. cm.