# CBSE Class 10-Mathematics: Chapter –13 Surface Areas and Volumes Part 7

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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 .

Abbreviation: Curved Surface Area TSA Total Surface Area

For cone, Radius of the base

Height

Volume of the solid V of hemisphere of cone

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).

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.

Abbreviation: CSA Curved Surface Area TSA Total Surface Area

Volume

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.

Let the volume of resulting sphere be .

According to question,