# The given figure represents a hemisphere surmounted by a conical block of wood.

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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

answered Mar 18 by (-11,659 points)

AC2 = AO2 + OC2

25 = AO2 + 9

AO2 = 16

AO = 4 cm

∴   Height of cone = 4 cm

(ii) Vol. of solid = Vol. of cone + Vol. of hemisphere

= 1/3πr2h + (4/3πr3)/2

= 1/3πr2h + 2/3πr3

= 1/3 × 22/7 × (3)2 × 4 + 2/3 × 22/7 × (3)3

= 37.68 + 56.52

= 94.20 cm3