Need help !
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 calculate the height of the
cone given that a hollow sphere of internal and external
diameters 4 cm and 8 cm respectively is melted into a
cone of base diameter 8 cm.
Given,
Internal diameter of hollow sphere = 4 cm
So, the internal radius of hollow sphere = 2 cm
External diameter of hollow sphere = 8 cm
So, the external radius of hollow sphere = 4 cm
We know that,
Volume of the hollow sphere 4/3 π × (43 – 23) … (i)
Also given,
Diameter of the cone = 8 cm
So, the radius of the cone = 4 cm
Let the height of the cone be x cm
Volume of the cone 1/3 π × 42 × h ….. (ii)
As the volume of the hollow sphere and cone are equal. We can equate equations (i) and (ii)
So, we get
4/3 π × (43 – 23) = 1/3 π × 42 × h
4 x (64 – 8) = 16 x h
h = 14