A manufacturer makes conical funnels for professional painters.
The funnels are formed from plastic with an 8-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 after the tip is cut off?

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

Step-by-step 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)

probability for j is 1/4

while

a is 1/6