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# 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 - ICSE Class 10 - Mathematics

ConceptVolume of a Combination of Solids

#### Question

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.

#### Solution

We have

Radius of the cylincler = 12/2 = 6cm

Height of the cylinder = 15cm

∴ volume of the cylinder = πr2h

= π x 62 x 15

= 540πcm3

Radius of the ice-cream cone = 3cm

Height of the ice-cream cone = 12cm

∴ valume of the conical part of ice-cream

cone = 1/3 pir^2h

valume of the conical part of ice-cream

cone = 1/3xxpixx3^2xx12cm^3

valume of the conical part of ice-cream

cone = 36πcm3

volume of the hemispherical top of the ice-cream =2/3pir^3=2/3xxpixx3^3]

= 18πcm3

Total volume of the ice-cream

cone = (36π+18π)cm3 = 54πcm3

∴ Number of ice-cream cone= "volume of the cylinder"/"Total volume of ice-cream"

=(540pi)/(54pi) = 10

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Ex. 14.20 | Q: 20 | Page no. 61
Solution 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 Concept: Volume of a Combination of Solids.
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