Question -
Answer -
Given,
The internal radius ofhollow sphere = 2 cm
The external radius ofhollow sphere = 4 cm
We know that,
Volume of the hollowsphere 4/3 π × (43 – 23) … (i)
Also given,
The base radius of thecone = 4 cm
Let the height of thecone be x cm
Volume of the cone 1/3π × 42 ×h ….. (ii)
As the volume of thehollow 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,
Slant height of thecone (l) is given by
l = √(h2 +r2)
l = √(142 +42) = √212
l = 14.56 cm
Therefore, the heightand slant height of the conical heap are 14 cm and 14.56 cm respectively.