CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Unless stated otherwise, take .

Question 2:

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to and the height of the cone is equal to its radius. Find the volume of the solid in terms of .

Answer:

Abbreviation: Curved Surface Area TSA Total Surface Area

For hemisphere, Radius

For cone, Radius of the base

Height

Volume of the solid V of hemisphere of cone

Volume of the Solid

Question 3:

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are by by . The radius of each of the depressions is and the depth id . Find the volume of wood in the entire stand (see figure) .

Answer:

Volume of the cuboid

Volume of conical depression

Volume of four conical depressions

Volume of the wood in the entire stand

Unless stated otherwise, take .

Question 4:

A metallic sphere of radius is melted and recast into the shape of a cylinder of radius . Find the height of the cylinder.

Answer:

Abbreviation: CSA Curved Surface Area TSA Total Surface Area

For sphere, Radius

Volume

For cylinder, Radius

Let the height of the cylinder be .

Then, Volume

According to question, Volume of sphere Volume of cylinder

Question 5:

Metallic spheres of radii , and 1 respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

Answer:

Let the volume of resulting sphere be .

According to question,

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