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NCERT Solutions Class 10 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.3 in Chapter 13 - Surface Areas and Volumes

Question 2 Surface Areas and Volumes - Exercise 13.3

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into 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:

Number of cones will be = Volume of cylinder / Volume of ice cream cone

For the cylinder part,

Radius = 12/2 = 6 cm

Height = 15 cm

∴ Volume of cylinder = π×r2×h = 540π

For the ice cone part,

Radius of conical part = 6/2 = 3 cm

Height = 12 cm

Radius of hemispherical part = 6/2 = 3 cm

Now,

Volume of ice cream cone = Volume of conical part + Volume of hemispherical part

= (⅓)×π×r2×h+(⅔)×π×r3

= 36π +18π

= 54π

∴ Number of cones = (540π/54π)

= 10

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