Q. 20

# A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.

Answer :

Given radius of cylinder (r’) = = 6 cm

Given radius of hemisphere (r’’) = =3 cm

Given height of cylinder (h) = 15 cm

Height of cone (l) = 12 cm

Volume of cylinder = πr^{2}h

= πr(6)^{2}(15) cm ………. (1)

Volume of each cone = Volume of cone + Volume of hemisphere

V = π(r)^{2}(l) + π(r)^{3}

V = π(3)^{2}(12) + π(3)^{3} ………… (2)

Let number of cone be n

n (volume of each cone) = volume of cylinder

n = [( π(3)^{2} (12) + π(3)^{3}] = π(16)^{2} 15

⇒ n = 10

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