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

Answer: 151

Step-by-step 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:

$V_{big}=\frac{\pi R^{2} H}{3}$

Where:

$R=\frac{Diameter}{2}=\frac{8 in}{2}=4 in$

$H=9 in$

Then:

$V_{big}=\frac{\pi (4 in)^{2} 9 in}{3}$

$V_{big}=150.79 in^{3}$ Volume of big cone

For the small cone:

$V_{small}=\frac{\pi r^{2} h}{3}$

Where:

$r=\frac{diameter}{2}=\frac{1 in}{2}=0.5 in$

$h=1 in$

Then:

$V_{small}=\frac{\pi (0.5 in)^{2} 1 in}{3}$

$V_{small}=0.261 in^{3}$ 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:

$V_{T}=150.52 in^{3} \approx 151 in^{3}$

Answer 2

Answer:

151 in^3

Step-by-step explanation:

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