A hollow sphere of external and internal diameters of 8 cm and 4cm respectively is melted and made into another solid in the shape of a right circular cone of base diameter 8 cm. Find the height of the cone.

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16 cm

4 cm

14 cm

15 cm

answer is C.

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Detailed Solution

Here , external diameter of follow sphere =8 cm internal diameter of follow sphere = 4 cm
8
Thus , External radius (R)=
4

= 4 cm
2
And Internal (r) =

= 2 cm
2
We know, the volume is given by =4(R3-r3)
3
So , on putting the values , we get
= 4 ( (4)3-(2)3)
3
𝜋
= 4x56 x
3
Accordingly ,hollow sphere is melted to a right circular flow of base diameter 8 cm
8
Radius of cone =
2

= 4 cm
The volume of cone
= 1 𝜋 (R)2 x h = 16h𝜋
3 3
Since , the slape of the follow sphere is changed into cone Volume of sphere = Volume of cone
𝜋
4x56
3
h=56
4

𝜋
= 16h
3
h= 14cm .

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