I would like to give a question which i could not solve.
Rd sharma class 10 maths exercise-16.1 mensuration.
In this question we have to find the diameter of the base of the cone having the surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm.
Need help
Given,
The height of the cone = 28 cm
Surface area of the solid metallic sphere = 616 cm3
We know that,
Surface area of the sphere = 4πr2
So, 4πr2 = 616
r2 = 49
r = 7
Radius of the solid metallic sphere = 7 cm
Let’s assume r to be the radius of the cone
We know that,
Volume of the cone = 1/3 πr2h
= 1/3 πr2 (28) ….. (i)
Volume of the sphere = 4/3 πr3
= 4/3 π73 ………. (ii)
On equating equations (i) and (ii), we have
1/3 πr2 (28) = 4/3 π73
Eliminating the common terms, we get
r2 (28) = 4 x 73
r2 = 49
r =7
So, diameter of the cone = 7 x 2 = 14 cm
Therefore, the diameter of the base of the cone is 14 cm