Given,
The internal radius of hollow sphere = 2 cm
The external radius of hollow sphere = 4 cm
We know that,
Volume of the hollow sphere 4/3 π × (43 – 23) … (i)
Also given,
The base 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
Now,
***** height of the cone (l) is given by
l = √(h2 + r2)
l = √(142 + 42) = √212
l = 14.56 cm
Therefore, the height and ** height of the conical heap are 14 cm and 14.56 cm respectively.*
