Question

A right circular metallic cone of height 20 m and radius of its base 5 cm is melted and recast into a sphere find the radius of the sphere

Answer 1

Given,

Height of cone, h = 20 cm

Radius of cone, r = 5 cm

∵ Volume of cone = 1/3TTr2h

= 1/3TT(5)2(20)

= 500TT/3 cm3

Now,

Radius of sphere, r = ?

∵ Volume of sphere = 4/3TTr3

Now,

Volume of sphere = Volume of cone

4/3TTr3 = 500TT/3

r3 = 125

r = 5 cm

So, radius of sphere = 5 cm

Answer 2

Question : A right circular metallic cone of height 20 m and radius of its base 5 cm is melted and recast into a sphere find the radius of the sphere ?


Method of Solution:

In this Question, It is Given that A right circular metallic cone of height 20 m and radius of its base 5 cm is melted and recast into a sphere.


We have:

✏ Height of Cone = 20 cm

✏ Radius of Cone = 5 cm

✒ •°• Volume of Cone = 1/3πr²h

✏ 1/3π(5)² × 20

✏ 500π/3



{ Formula of Sphere }

✏ Volume of Sphere = 4/3πr³

Now, According to the Question!


[ Statement : It recast into a sphere ]


Volume of Cone = Volume of Sphere


✏ 500π/3 = 4/3πr³

✏ 500/3 = 4/3 × r³

✏ 166.66 = 1.33 × r³

✏ 125 = r³

✏ r = ³√125

✏ Radius = 5 Centimeters


Hence, Required Value of Radius of Sphere is 5 Cm.