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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:
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 .