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
(i) In △ADC
AC^{2} = AO^{2} + OC^{2}
25 = AO^{2} + 9
AO^{2} = 16
AO = 4 cm
∴ Height of cone = 4 cm
(ii) Vol. of solid = Vol. of cone + Vol. of hemisphere
= 1/3πr^{2}h + (4/3πr^{3})/2
= 1/3πr^{2}h + 2/3πr^{3}
= 1/3 × 22/7 × (3)^{2} × 4 + 2/3 × 22/7 × (3)^{3}
= 37.68 + 56.52
= 94.20 cm^{3}