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Q.

A hollow sphere of internal and external diameters of 4 cm and 10 cm respectively, is melted into a cone of base diameter 5 cm. ____ is the height of the cone so formed.

Chapter/Topic: Surface Areas and Volumes

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Detailed Solution

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Here, the hollow sphere is melted to form a cone. The radius of the base of the cone is half of its diameter, that is r = d/2
Substituting d= 5cm in the formula, we get
Radius of the base of the cone =5/2 cm.
Substituting d= 4cm in the formula, we get
Internal radius of the sphere =4/2=2 cm.
Substituting d=10cm in the formula, we get
External radius of the sphere =10/2=5 cm.
Now, we need to find out the external and internal volume of the sphere.
We know that the formula of the volume of a sphere is

\frac{4}{3} π r^{3}

So, the volume of the material of the hollow sphere is used to make the cone.
Volume of hollow sphere = Volume of the cone
6π(D3 −d3) =

\frac{1}{3}

πr2h
6π( 103 −53) =

\frac{1}{3}

π(2.5)2h
h =

\frac{125}{12.5}

h =10 cm

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