The base of a 6-inch long ice cream cone with a diameter of 2 inches, is cut 0.25 inches from the base. The left over shape resembles a cylinder. What is the BEST estimate for this shape's volume?

volume of 6" cone minus volume of 4" cone

diameter of 6" cone = 2"
diameter of 4" cone = 4/3 "

now just plug and chug

To find the volume of a shape resembling a cylinder, we need to first calculate the radius of the base of the leftover shape.

The diameter of the original base is given to be 2 inches. Since the base was cut 0.25 inches from the bottom, we subtract 0.25 inches from the original height of 2 inches to find the new height:

2 inches - 0.25 inches = 1.75 inches

Next, we need to find the new radius of the base. The radius of the original base is half of the diameter, which is 2 inches / 2 = 1 inch. Similarly, the new radius is the height of the leftover shape divided by 2.

1.75 inches / 2 = 0.875 inches

Now we can use the formula for the volume of a cylinder to estimate the volume of the leftover shape:

Volume = π * r^2 * h

where π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the shape.

Plugging in the values:

Volume = 3.14159 * (0.875 inches)^2 * 1.75 inches

Calculating the expression on the right would give you the best estimate for the shape's volume.