Question

A manufacturer makes conical funnels for professional painters. The

funnels are formed from plastic with an 8-inch diameter base and height
of 9 inches. After the cones cool, a machine cuts off 1 inch of the tip to
leave a 1-inch diameter hole in the end. What is the volume of the funnel?
Round your answer to the nearest tenth and do NOT include units.

Answer 1

151 in^3

Explanation:

Find the volume of the cones the subtract them to get your final answer

Answer 2

Answer: 151

Explanation:

In this situation we have two cones, the big cone with volume
`V_(big)` and the small cone with volume
`V_(small)`.

Now, if we want to know the total volume
`V_(T)` we have to substract
`V_(small)` from
`V_(big)`, but first we have to calculate each volume:

For the big cone:

`V_(big)=(\pi R^(2) H)/(3)`

Where:

`R=(Diameter)/(2)=(8 in)/(2)=4 in`

`H=9 in`

Then:

`V_(big)=(\pi (4 in)^(2) 9 in)/(3)`

`V_(big)=150.79 in^(3)` Volume of big cone

For the small cone:

`V_(small)=(\pi r^(2) h)/(3)`

Where:

`r=(diameter)/(2)=(1 in)/(2)=0.5 in`

`h=1 in`

Then:

`V_(small)=(\pi (0.5 in)^(2) 1 in)/(3)`

`V_(small)=0.261 in^(3)` Volume of small cone

Calculating the total volume:

`V_(T)=V_(big)-V_(small)`

`V_(T)=150.79 in^(3)-0.261 in^(3)`

Finally:

`V_(T)=150.52 in^(3) \approx 151 in^(3)`