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# A hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted into a cone of base diameter 8 cm. Find the height of the cone.

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ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
In this question,
A hollow sphere of internal and external diameters are given, is melted into a cone of given base diameter .
You have to find the height of the cone.
This is the Question Number 13, Exercise 17.5 of M.L Aggarwal.

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### 1 Answer

1. Given internal diameter of hollow sphere = 4 cm

Internal radius, r = 4/2 = 2 cm

External diameter = 8 cm

External radius, R = 8/2 = 4 cm

Volume of the hollow sphere, V = (4/3)(R3-r3)

V = (4/3)Ã—(43-23)

V = (4/3)Ã—(64-8)

V = (4/3)Ã—56

Base diameter of the cone = 8 cm

Radius, r = 8/2 = 4 cm

Volume of cone = (1/3)r2h

= (1/3)Ã—42Â Ã—h

= (16/3)Ã—h

Since sphere is melted and changed into a cone, their volumes remain same.

(4/3)Ã—56 = (16/3)Ã—h

h = 4Ã—56/16

h = 14 cm

Hence the height of the cone is 14 cm.

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