Question

Aaron drew a cone that has a volume of 90in.If Armani drew a cylinder with the same

base and height as Aaron's cone, what is the
volume of her cylinder? Explain your
reasoning.

Answer 1

Vol_cylinder = 270 cubic inches

Explanation:

Aaron's cone has the Volume

= 1/3BaseArea•height

Armani's Cylinder Volume

= BaseArea•height

The only difference here is the 1/3 in the cone formula.

So the cone volume is 1/3 of the cylinder volume. Or the cylinder volume is 3times the cone volume.

Vol_cone = 90

Vol_cyl = 3•90 = 270

90 is 1/3 of 270.

The cylinder volume is 270 cubic inches.

Answer 2

Explanation:

A cone has a volume formula of
`(1)/(3) \pi r^(2) h`

A cylinder has a volume formula of
`\pi r^(2) h`

So if both of the shapes have the same base and height as in 'h' and 'r' are equal, than the cone has 1/3 the volume of the cylinder.

Thus:

`V_(cone) =(1)/(3) V_(cylinder) \\90 = (1)/(3) V_(cylinder)\\V_(cylinder) = 270`

Thus the volume of the cylinder is 270 cubic inches.

Hope that helps!