Question

A frustum of a cone is the part that remains when the top of the cone is cut off by a plane parallel to the base.

A popcorn container 9 in. tall is the frustum of a
cone. Its small radius is 4.5 in. and its large radius is 6 in. What is its volume?

Answer 1

1. find the volume of a cone that doesn't have the top cut off and has a base of 6in radius
2. find the volume of a cone that has a radius of 4.5in base
3. find the difference of volume from step 1 and step 2. this is the volume of the frustum.

Answer 2

\[V=\frac{ 1 }{ 3 }\pi (6^2)(9)\]
\[V=\frac{ 1 }{3 }\pi (36)(9)\]\[V=\frac{ 1 }{3 }\pi (324)\]
\[V= (108)\pi\]
\[V=339.29\]

for cone with no top cut off

Answer 3

is the cone 9 inches tall or just the popcorn container?

Answer 4

it says the container
but i dont get how to do it any other way

Answer 5

oh ok

Answer 6

h = 9+y

use similar triangles:
h:6 as y:4.5
or
h/6 = y/4.5
replace h with the eq 9+y

(9+y)/6 = y /4.5
solve for y

Answer 7

ok

Answer 8

*hint y will be near 25

Answer 9

i gotta go, but i'll give you some hints/help:
remember how I wrote this:

1. find the volume of a cone that doesn't have the top cut off and has a base of 6in radius
2. find the volume of a cone that has a radius of 4.5in base
3. find the difference of volume from step 1 and step 2. this is the volume of the frustum.


for step 1, use r=6 and h = 9+27
for step 2, use r=4.5 and h=27