Question

A tag is in the form of a hemisphere surmounted by a right circular cone of same base radius as that of the hemisphere. If the radius of the base of cone is 21cm and its volume is 2/3 of volume of hemisphere calculate height of cone and surface area of toy?

Answer 1

Given radius of cone = radius of hemisphere

Radius (r) = 21cm

Given that volume of cone =2/3 Volume of hemisphere

l = √(h² + r²)

l = √(28² + 21²)

l = √(784 + 441)

l = √(1225)

l = 35cm

S₁ = π(21)(35) cm²

S₁ = 2310 cm²

Curved surface area off hemisphere = 2πr²

S₂= 2 x π(21)²

S₂ = 2772 cm²

Total surface area (S) = S₁ +S₂

= 2310 + 2772 = 5082 cm²

Curved surface area of toy = 5082 cm²