Question

The volume of a cylinder is 300 feet3. Find the volume of a cone and a sphere that have the same height and radius as the cylinder.PLEASE HELP IS DUE TOMORROW.THANKS

Answer 1

The formula of a volume of a cylinder:

$V_{cylinder}=\pi r^2H$

The formula of a volume of a cone:

$V_{cone}=\dfrac{1}{3}\pi r^2H$

Therefore, if a cone has the same radius and height like a cylinder, then the volume of a cone is three times smaller than the volume of a cylinder.

Therefore we have:

$V_{cone}=\dfrac{1}{3}V_{cylinder}\to V_{cone}=\dfrac{1}{3}(300)=100\ ft^3$

The formula of a volume of a sphere:

$V_{sphere}=\dfrac{4}{3}\pi R^3$

If a cone has that same lengths of a radius and a height, then the formula of a volume is:

$V_{cone}=\dfrac{1}{3}\pi r^2r=\dfrac{1}{3}\pi r^3$

If a cone and a sphere have the same radius, then the volume of a sphere is four times greater than a volume of a cone.

Therefore we have:

$V_{sphere}=4(100)=400\ ft^3$