Question

Twelve solid spheres of the same sizes are made by melting a solid metallic cylinder of base diameter 2 cm and height 16cm. Find the radius of each sphere.

Answer 1

SOLUTION:

Given:
Diameter of a solid metallic cylinder(d) = 2 cm
Height of a solid metallic cylinder (h)= 16 cm

Radius of a solid metallic cylinder (r)=  d/2 = 2/2 = 1 cm.

Let the radius of a solid sphere = R
Solid metallic cylinder is melted to form a  12 solid spheres.
So, volume of twelve solid spheres will be equal to the volume of solid metallic cylinder.

volume of 12 solid spheres = volume of solid metallic cylinder.
12×(4/3)πR³ = πr²h
16R³ = 1² × 16
R³ =1

R = 1 cm.

Hence , the radius of each sphere is = 1 cm.

HOPE THIS WILL HELP YOU..

Answer 2

Diameter of cylinder = 2 cm

Radius = 1 cm

Height = 16 cm

Volume of cylinder = pi r^2 h

= pi × 1 × 16

= 16 pi


Now,

Volume of 12 sphere = Volume of cylinder

=> Volume of 12 sphere = 16 pi

=> Volume of 1 sphere = 16 pi / 12

=> 4/3 pi r^3 = 4pi /3

=> r^3 = 1

=> r = 1

Radius of each sphere = 1 cm