Question

A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole
ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base
surmounted by hemispherical top. If the height of conical portion is twice the diameter of
base, find the diameter of conical part of ice-cream cone.​

Answer 1

Diameter of cylindrical tub, 12cm

Radius, R = 12/2 = 6cm

Height, H = 15cm

Volume of cylindrical = π R2H

= 22/7 x 6 x 6 x 15

For conical portion, let radius, r and diameter, d cm

Height = 2d = 4r

For hemisphere part r1 = r cm

Total volume of ice cream = vol. of cone + vol. of hemisphere

= 1/3 π r2h + 2/3 π r13

= 1/3 π r2 (h+2r) (because r1=r)

= 1/3 x 22/7 x r2 x (4r+2r)

= 44/7 x r3

Therefore, 10 x 44/7 x r3 = 22/7 x 6 x 6 x 15

r3 = 22/7 x 6 x 6 x 15 x 7/44 x 1/10

r3 = 27

r = 3 cm

d = 6 cm

Answer 2

15 cm is full of ice-cream. The whole

ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base

surmounted by hemispherical top

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