Question

A metallic cylinder of diameter 5cm and height 10\3 cm. Melted and cast into a sphere. What is it’d diameter.?

Answer 1

Sol:
Diameter of the cylinder = 5 cm
Radius = 5/2 cm
Height of the cylinder = 10/3 cm
Volume of the cylinder = π r2h
= π (5/2)(5/2)10/3)

Let the radius of the sphere be 'r' cm
Volume of the sphere = 4/3 π r3

Volume of the sphere = Volume of the cylinder
4/3 π r3 = π (5/2)(5/2)10/3)

r3 = (5/2)(5/2)10/3)(3/4)
r3 = (125 / 8)
r3 = 53 / 23
r = 5/2
r = 2.5 cm

Therefore, radius of the sphere is 2.5 cm.

Answer 2

after putting ,
volume of cylinder = volume of sphere
you will get radius and
diameter =2×radius.