Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer 1

Given 

radius of cone (r) = 3.5 cm 

Total height of toy (h) = 15.5 cm 

height of cone (l) = 15.5 – 3.5 

= 12 cm 

As we know, 

l² = r² + h² 

= 3.52 + 12² 

The curved surface area of a cone,S’ = πrl 

= π (3.5) (12.5) 

= 137.5 cm²…….. (1) 

The curved surface area of the hemisphere, S’’ = 2πr² 

= 2π(3.5)² 

= 77 cm²………… (2)

∴ Total surface area of the toy = 137.5 + 77 = 214.5 cm²