Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 m3

Answer 1

Volume of cylinder = pi r^2 h = 30 m^3
Volume of sphere = 4/3 pi r^3
now h = 2r ( given)
so volume of cylinder = pi r^2 * 2r = 2 pi r^3 = 30
pi r^3 = 15 so r^3 = 15/pi

therefore the volume of sphere = 4/3 pi * 15/pi = 4/3 * 15 = 20 m^3 Answer

Answer 2

Option B is correct

`20 m^3`

Explanation:

Volume of the sphere(V) is given by:

`V = (4)/(3) \pi r^3`; .....[1] where, r is the radius of the sphere.

Volume of cylinder(v') is given by:

`V'= \pi r'^2h'`

where, r' is the radius of the cylinder and h' is the height of the cylinder

As per the statement:

A sphere and a cylinder have the same radius and height.

r = r'

h = 2r = h'

It is also given that: The volume of the cylinder is 30 m^3

⇒
`V' = \pi r'^2h'`

⇒
`30 = \pi r^2 \cdot (2r)`

⇒
`30 = 2 \pi r^3`

Divide both sides by 2 we have;

`15 = \pi r^3`

Substitute in [1] we have;

`V = (4)/(3) \cdot 15`

Simplify:

`V = 20 m^3`

Therefore, volume of sphere is,
`20 m^3`