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:

Radius of the cone and hemisphere (r) = 9 cm

Height of cone (h) = 12 cm

π = 3.14

1. Slant Height of Cone (l):

`l = sqrt(r^2 + h^2)` 

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

= `sqrt(81 + 144)`

= `sqrt(225)`

= 15 cm

2. Total Surface Area of the Toy:

Total Surface Area = CSA of Cone + CSA of Hemisphere

TSA = πrl + 2πr²

= πr(l + 2r)

= 3.14 × 9 × (15 + 2 × 9)

= 3.14 × 9 × (15 + 18)

= 3.14 × 9 × 33

= 3.14 × 297

= 932.58 cm²