Question -
Answer -
Given,
The height of the cone= 28 cm
Surface area of thesolid metallic sphere = 616 cm3
We know that,
Surface area of thesphere = 4πr2
So, 4πr2 =616
r2 =49
r = 7
Radius of the solidmetallic sphere = 7 cm
Let’s assume r to bethe 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 commonterms, we get
r2 (28)= 4 x 73
r2 =49
r =7
So, diameter of thecone = 7 x 2 = 14 cm
Therefore, thediameter of the base of the cone is 14 cm