Question

A cylinder has a volume of 405 units if a cone has the same radius and the same height as the cylinder how many cubic units is the volume of the cone

Answer 1

Answer:

Therefore,

Volume of the cone is 135 cubic units.

Step-by-step explanation:

Given:

Volume of Cylinder = 405 units³

Radius and Height are same for both Cone and Cylinder

To Find:

Volume of Cone = ?

Solution:

We know that

$\textrm{Volume of a Cylinder}=\pi (Radius)^{2}\times Height$

And

$\textrm{Volume of a Cone}=\dfrac{1}{3}\pi (Radius)^{2}\times Height$

Dividing the two volumes we get

$\dfrac{\textrm{Volume of a Cylinder}}{\textrm{Volume of a Cone}}=\dfrac{\pi (Radius)^{2}\times Height}{\dfrac{1}{3}\pi (Radius)^{2}\times Height}$

On Cancellation as Radius and Height are same for both Cone and Cylinder we get

$\textrm{Volume of a Cone}=\dfrac{1}{3}\times \textrm{Volume of a Cylinder}$

Substituting the values we get

$\textrm{Volume of a Cone}=\dfrac{1}{3}\times 405=135\ units^{3}$

Therefore,

Volume of the cone is 135 cubic units.