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

Answer:

Option B is correct

$20 m^3$

Step-by-step explanation:

Volume of the sphere(V) is given by:

$V = \frac{4}{3} \pi r^3$;     .....[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;

$V = \frac{4}{3} \cdot 15$

Simplify:

$V = 20 m^3$

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