Question

A cone of hight 8.4 cm and radius of base 2.1 cm us melted into sphere.The diameter of sphere will be

Answer 1

Answer:

Solution :

Given ,height of a cone = 8.4 cm

Radius of the base of cone = 2.1 cm

Volume of a cone =13πr2h=13×π×(2.1)2×8.4

=13×π×2.1×2.1×8.4=π×4.41×2.8cm3

Since, cone is melted and recast into a sphere.

Let the radius of a sphere be R.

Thlen, volume of a sphere = Volume of a cone

⇒ 43πr3=π×4.41×2.8⇒r3=4.41×2.8×34

⇒ r3=4.41×0.7×3

⇒ r3=4.41×2.1

∴ r=2.1

Hence , the radius of the sphere is 2.1 cm.

since the radius of the sphere is 2.1 cm

diameter = 2.1×2

= 4.2

therefore the diameter of the sphere is 4.2 cm.

Answer 2

Radius of the base = the radius of the sphere

Diameter = 2 *2.1cm = 4.2cm