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# A Solid Toy is in the Form of a Hemisphere Surmounted by a Right Circular Cone. Height of the Cone is 2 Cm and the Diameter of the Base is 4 Cm. If a Right Circular Cylinder Circumscribes the Toy, Find How Much More Space It Will Cover. - CBSE Class 10 - Mathematics

ConceptVolume of a Combination of Solids

#### Question

A solid toy is in the form of a hemisphere surmounted by a right circular cone. height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find  how much more space it will cover.

#### Solution

Let r1 r2 and r3 cm denate the radii of the base of the cylinder, cone and hemisphere respectively. Then,

r1 = r2 = r3 = 4/3 =2 cm

Let h1 and l cm be the heights of the cylinder and cone respectively. Then,

h = 4cm and l= 2cm

s0, the remaining volume of the cylinder when the toy is inserted into it.

= Volume of the cylinder -(volume of the cone + volume of the hemisphere)

= pir_1^2h-(1/3pir_2^2l+2/3pir_3^3)

=pixx(2)^2xx4-(1/3pixx(2)^2xx2+2/3pixx(2)^3)

=16pi-((8pi)/3+(16pi)/3)

=16pi-((24pi)/3)

=16π - 8π

= 8π cm3

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: 22 | Page no. 61
Solution A Solid Toy is in the Form of a Hemisphere Surmounted by a Right Circular Cone. Height of the Cone is 2 Cm and the Diameter of the Base is 4 Cm. If a Right Circular Cylinder Circumscribes the Toy, Find How Much More Space It Will Cover. Concept: Volume of a Combination of Solids.
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