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.
Deepak BoraNewbie
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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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)×(43-23)
V = (4/3)×(64-8)
V = (4/3)×56
Base diameter of the cone = 8 cm
Radius, r = 8/2 = 4 cm
Volume of cone = (1/3)r2h
= (1/3)×42 ×h
= (16/3)×h
Since sphere is melted and changed into a cone, their volumes remain same.
(4/3)×56 = (16/3)×h
h = 4×56/16
h = 14 cm
Hence the height of the cone is 14 cm.