Question

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy.(use π = \(\frac{22}7\))

Answer 1

Radius of base = 21cm and its volume = \(\frac{2}3\) × volume of the hemisphere 

⇒ \(\frac{1}3\)πr²h = \(\frac{2}3\times\frac{2}3\)πr³

⇒ h = \(\frac{4}3r\) = \(\frac{4}3\times21\) = 28 cm

Hence 

surface area of the toy = Surface area of the cone + Surface area of hemisphere 

= π r (\(\sqrt{21^2 + 28^2}\)) + 2π r² 

= π (21)[35 + 2 × 21] 

= 5082 cm²