Question

Find the volume of a cylinder with base area 196 cm2 and a height equal to the diameter

Answer 1

Hello!

The answer is:

The volume of the cylinder is equal to:

`Volume=3096.8cm^(3)`

Why?

To find the volume of the cylinder, first, we need to use the equation to calculate its area to find its diameter, and then, calculate its volume since we know that the height of the cylinder is equal to its diameter.

So, using the equation to calculate the area of its base, we have:

`BaseArea=\pi *r^(2)\\\\r=\sqrt{(BaseArea)/(\pi ) }=\sqrt{(196cm^(2) )/(\pi )}\\\\r=\sqrt{(196cm^(2) )/(\pi )}=\sqrt{62.4cm^(2)}=7.9cm`

Therefore, we have that the radius of the cylinder is equal to 7.9 cm, it means that its diameter is equal to:

`diameter=2*radius=7.9cm*2=15.8cm`

Now that we know the diameter, let's calcule the volume of the cylinder:

`Volume=BaseArea*height=BaseArea*Diameter\\\\Volume=196cm^(2)*15.8cm=3096.8cm^(3)`

Hence, we have that the volume of the cylinder is equal to:

`Volume=3096.8cm^(3)`

Have a nice day!