Mathematics: The volume of a cylinder is 180 cubed meters. What is the volume of a cone with the same radius and height as the cylinder?

It would be an 18 Step-by-step explanation:You re welcome...

The volume of a cylinder is 180 cubed meters. What - id1806785000, heleneallie7ou1fnk

jackvj4959

28.01.2022

60 cubic meters will be the volume of such cone.

Step-by-step explanation:

Formula for volume of a cylinder:

$V = \pi r^{2} h ...... (1)$

Where is the radius of base of cylinder

and is the height of cylinder

V = 180 cubic meters

Formula for volume of a cone:

$V' = \dfrac{1}{3}\pi R^{2} H ...... (2)$

Where is the radius of base of cone

and is the height of cone

Now, it is given that height and radius of cone are equal.

$r = R\\h =H$

Putting the values in equation (2):

$V' = \dfrac{1}{3}\pi r^{2} h$

Using equation (1):

$V' = \dfrac{1}{3} \times V$

Putting V = 180 cubic meters

$\Rightarrow V' = \dfrac{1}{3} \times 180\\\Rightarrow V'=60 \text { cubic meters}$

Hence, 60 cubic meters will be the volume of such cone.

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