A cylindrical block of cheese has a 6-inch diameter and is 2 inches thick. After a party, only a sector remains that has a central angle of 45 degrees. Find the volume of the cheese that remains. Show all work

Answer: The volume of cheese remaining is 7 cubic inches (7 in³)

Step-by-step explanation: The cheese is in the shape of a cylinder. The volume of a cylinder is given as follows;

Volume = πr²h

Where r = radius of the top of the cylinder and h = the height of the cylinder.

In this case, the cheese has its radius as 3 inches (that is diameter divided by 2). Also the height is given as the thickness of the cheese which is 2 inches. Note also that part of the cylindrical cheese has been eaten leaving only a potion which has an angle of 45 degrees.

The volume of the left over portion therefore can be calculated as follows;

Volume = (∅/360) x πr²h

Volume = (45/360) x 3.14 x 3² x 2

Volume = (1/8) x 3.14 x 9 x 2

Volume = (1/8) x 56.52

Volume = 7.065

Volume ≈ 7

Therefore the volume of cheese that remains is 7 cubic inches (7 inches³) approximately.