Acylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm. what is the height of the cone

Volume of cylinder(V) is given by:

where,

r is the radius and

h is the height of the cylinder.

Volume of cone(V') is given by:

where, r' is the radius and h' is the height of the cone.

As per the statement:

A cylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm

⇒r = 12 cm , h = 20 cm and r' = 8 cm

Since, Volume of cylinder is equal to Volume of cone.

⇒V  = V'

then;

⇒

Substitute the given values to solve for h' we have;

⇒

Multiply both sides by 3 we have;

⇒

⇒

Divide both sides by 64 we have;

or

h' = 135 cm

Therefore, the height of the cone is, 135 cm

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step-by-step explanation:

at least i think its