260,972 views
16 votes
16 votes
10. A manufacturer makes conical funnels for

professional painters. The funnels are
formed from plastic with a 9-inch
diameter base and a 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? Show your work.

10. A manufacturer makes conical funnels for professional painters. The funnels are-example-1
User Lavande
by
3.0k points

1 Answer

15 votes
15 votes

Answer:

The volume of the cone after the tip is cut off equals 150 cubic inches

Explanation:

The dimensions of the cone formed from the funnel are given as height equals 9 inches and, radius equals 4 inches (radius = 8/2).

The volume of a cone is determined as follows;

Volume = πr²h/3

Volume = π x 4² x (9/3)

Volume = π x 16 x 3

Volume = 48π

When a portion of the cone is cut off from the tip, the height from the cut off part is 1 inch and the radius is 0.5 inch (radius = 1/2).

The volume of the cut off portion can now be calculated as;

Volume = πr²h/3

Volume = π x 0.5² x (3/3)

Volume = π x 0.25 x 1

Volume = 0.25π

Hence the volume of the cone after the tip has been cut off is now derived as follows;

Volume = 48π - 0.25π

Volume = 47.75π

Volume = 47.75 x 3.14

Volume = 149.935

Volume ≈ 150 cubic inches (Rounded to the nearest whole number)

I hope this helps :)

User Entoarox
by
2.9k points