A cone has a base area of 33 in2 and is 8 inches tall. What is the volume of the cone in cubic inches

Vcone = 1/3 × b × h

V = (1/3) * 33 * 8

V = 88 cu. in.

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To calculate the volume of a cone, you need two measurements: the base area and the height. In this case, you have the base area of 33 in² and the height of 8 inches.

The formula to calculate the volume of a cone is:

Volume = (1/3) * π * r² * h

where π represents pi, r is the radius of the base, and h is the height of the cone.

To find the radius, you'll need to know the radius of the base, which is half the diameter. Unfortunately, the radius is not given directly in the question. However, you have the base area, which is related to the radius.

The formula for the area of a circle is:

Area = π * r²

Therefore, you can use the area formula to find the radius:

33 in² = π * r²

To isolate the radius, divide both sides of the equation by π:

33 in² / π = r²

Now, take the square root of both sides to solve for r:

√(33 in² / π) = r

Now that you have the radius, you can substitute it and the height into the volume formula to find the volume of the cone.

Volume = (1/3) * π * r² * h

Volume = (1/3) * π * (√(33 in² / π))² * 8 in

Volume = (1/3) * π * (33 in² / π) * 8 in

Simplifying the equation:

Volume ≈ (8/3) * 33 in³

Volume ≈ 88 in³

Therefore, the volume of the given cone is approximately 88 cubic inches.