Question

cone A is similar to cone B cone A has a radius equal to 6 inches in Cone B has a radius equal to 13 in if the volume of cone is 252 in what is the volume of a Cone B

Answer 1

If cone A is similar to cone B, this means that the ratio height/radius is the same in both cones. The formula for the volume of a cone is pi times r^3 times height times 1/3. The measures of the cones known so far are the following:

`r_a=6\text{ in}`
`r_b=13\text{ in}`
`v_a=252in^3`
`v_a=252=(1)/(3)\cdot\pi\cdot6^3\cdot h_a`

Then, the height of cone a can be found as:

`h_a=252\cdot3\cdot(1)/(\pi\cdot216)\cong1.11`
`(1.11)/(6)=(h_b)/(13)\Rightarrow h_b=2.41`
`v_b=\pi\cdot(1)/(3)\cdot2.41\cdot13^3=5533.5in^3`