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NCERT Class 10 Mathematics Solutions: Chapter 13- Areas and Volumes Exercise 13.3 Part 1

Illustration: NCERT Class 10 Mathematics Solutions: Chapter 13- Areas and Volumes Exercise 13.3 Part 1

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

Answer:

Radius () of hemisphere

Radius () of cylinder

Consider, the height of the cylinder be .

Volume of sphere = Volume of cylinder

So, the height of the cylinder so formed will be .

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

Answer:

Radius () of 1st sphere

Radius () of 2nd sphere

Radius () of 3rd sphere

Consider, the radius of the resulting sphere be .

The object formed by recasting these spheres will be same in volume as the sum of the volumes of these spheres.

Volume of 3 spheres = Volume of resulting sphere

So, the radius of the sphere so formed will be 12 cm.

3. A deep well with diameter is dug and the earth from digging is evenly spread out to form a platform by . Find the height of the platform. [Use ]

Answer:

A Cylinder Figure Are Shown

The shape of the well will be cylindrical.

Depth () of well

Radius () of circular end of well

Area of platform = Length Γ— Breadth

Let height of the platform

Here, volume of soil dug from the well will be equal to the volume of soil

Volume of soil from well = Volume of soil used to make such platform

So, the height of such platform will be .