Question

The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each and the slant height of the cone is 5 cm. Calculate:
(i) the height of the cone.
(ii) the vol. of the solid.

Answer 1

(i) In Δ ADC,
AC² = AO² + OC²
25 = AO² + 9
AO² = 25 - 9
AO = 4 cm
∴ Height of cone = 4 cm

(ii) Volume of solid = Volume of cone + Volume of hemisphere
= `1/3 πr^2h + (4/3πr^3)/2`

= `1/3 πr^2h + 2/3 πr^3`

= `1/3 xx 22/7 xx (3)^2 xx 4 + 2/3 xx 22/7 xx (3)^3`
= 37.68 + 56.52 
= 94.20 cm³