Question

The radius of the cone is 10 cm. A sphere has the same radius and same volume as that of
the cone. Find the total surface area of the cone (Take π=3.14)

Answer 1

Radius of cone = 10 cm
Radius of sphere = 10 cm
Volume of sphere = 4 pi r^3 / 3
= 4 *pi *1000/3
= 4000pi /3

According to question
Volume of cone = Volume of sphere
pi *r^2 *h / 3= 4000pi/ 3
=> 100 h = 4000
=> h = 40 cm

Now,
Slant Height = square root (40^2 + 10^2)
L = square root (1600+100)
L = 41.23 cm

Total Surface Area = pi *10(41.23 + 10)
= 3.14*10 * 51.23
= 1608.66 cm^2