Question

A toy is in the form of a cone surmounted on hemisphere. The diameter of the base and height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy. (Use $\pi =3.14)$

Answer 1

Given :
For cone -
Height of the cone = 4cm
Diameter of the cone = 6cm
Radius of the cone = 3cm
Slant height of the cone l = $\sqrt{r^2+h^2}$
⇒ l = $\sqrt{3^2+4^2}$
⇒ l = 5
Lateral surface area of the cone = πrl
⇒ 3.14 × 3 × 5
⇒ 3.14 × 15
⇒ 47,10 cm²

For Hemisphere -
1. Diameter of the hemisphere = 6cm
2. Radius of hemisphere = 3cm
Lateral surface area of hemisphere = 2πr²
⇒ 2 × 3.14 × 3²
⇒ 2 × 3.14 × 9
⇒ 18 × 3.14
⇒ 56.52 cm²

The surface are of toy = lateral surface area of cone + lateral surface area of hemisphere
= 47.10 + 56.52
= 103.62 cm²

∴ The total surface area of toy = 103.62 cm²