Question

In the given figure, a toy made from a hemisphere, a cylinder and a cone are shown. Find the total area of the toy.

Answer 1

Radius of the sphere = Radius of the cylinder = Radius of cone = r = 3 cm
Height of the cone, h = 4 cm
Height of the cylinder, H = 40 cm 
Let the slant height of the cone be l cm.

l² = r² + h²

= 3² +4²

= 9 + 16

= 25

l = `sqrt25`

∴ l = 5 cm

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

\[= 2\pi r^2 + 2 \pi rH + \pi rl\]
\[ = 2\pi \times \left( 3 \right)^2 + 2\pi \times 3 \times 40 + \pi \times 3 \times 5\]
= 2π × 9 + 240π + 15π

= 18π + 240π + 15π

= 273π cm²

Thus, the total area of the toy is 273π cm².