twelve solid spheres of the same size are made by melting a solid metallic cylinders of base diameter 2cm and height 16cm. find the radius of each sphere
Answers
Height of cylinder (H) = 16cm
Let, the radius of small spheres be rcm
So,
12(volume of small sphere) = volume of cylinder
=> 12(4/3πr^3) = πR^2H
=> 16r^3 = 1^2 × 16
=> r^3 = 1cm
=> r = 1cm.
Given,
The base diameter of cylinder = 2 cm
Height of the cylinder = 16 cm
To find,
We have to find the radius of the sphere.
Solution,
The radius of each sphere when twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm is 1 cm.
We can simply find the radius of each sphere by using the relation,
The volume of a cylinder = Volume of 12 solid spheres
The volume of cylinder = πR²h
The volume of a sphere = 12 *4/3 πr³
π * 2/2 * 2/2 * 16 = 12* 4/3 * π * r³
16 = 16 * π * r³
1 = r³
r = 1
Hence, the radius of each sphere when twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm is 1 cm.