Question

a toy is in the form of a cone mounted on a hemi sphere. the diameter of the base and the cone are 6cm and4cm respectively. determine the surface area of the toy.

Answer 1

Given :
 For cone -
1. Height of the cone = 4cm
2. diameter of the cone = 6cm
3.radius of the cone = = 6/2 = 3cm
Slant height of the cone l = √r²+h²
⇒ l = √3²+4²
⇒ l = √9+16
⇒ 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 = 6/2 = 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
⇒ 103.62cm³ 

∴ The total surface area of toy = 103.62cm³

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