Question

A toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone and that of a hemisphere is 18 cm and the height of cone is 12 cm. Find the total surface area of toy. (π = 3.14)

Answer 1

Given:

Diameter of base = 18 cm → radius r = 9 cm.

Height of cone h = 12 cm.

Take π = 3.14.

Step-wise calculation:

1. Slant height `l` of the cone: `l = sqrt(r^2 + h^2)` 

= `sqrt(9^2 + 12^2)`

= `sqrt(81 + 144)`

= `sqrt(225)`

= 15 cm

2. Formula for total surface area of the toy cone mounted on hemisphere: 

Total surface area = Curved surface area of cone + Curved surface area of hemisphere

= πrl + 2πr²

3. Compute each term:

Curved surface area of cone = πrl

= π × 9 × 15

= 135π

Curved surface area of hemisphere = 2πr² 

= 2 × π × 9²

= 162π

Total (symbolic) = 135π + 162π

= 297π

4. Numeric value using π = 3.14:

Total surface area = 297 × 3.14

= 932.58 cm²

Total surface area of the toy = 297π cm²

= 932.58 cm²