I have to calcualte the volume of a cone. The height is 2.1 ft, and the base is 2 inches.
I keep coming up with the answer of 8.792 cu ft.
There is 4 choice answers given: 0.061 ft,0.610 ft,6.125 ft and 2.016 ft.
I have tried several calculators, none of these answers are coming up as a solution.
Any help?
if we want the answer in ft^3, then let's convert the base to ft. I assume that's the radius of the base.
v = 1/3 pi r^2 h
= 1/3 pi (1/6)^2 * 2.1
= 0.061 ft^3
Looks like (A)
To calculate the volume of a cone, you can use the formula: V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
First, let's convert the height and base measurements into the same unit. The height is given as 2.1 ft, but the base diameter is given as 2 inches. To convert inches to feet, divide by 12 since there are 12 inches in a foot. So, the base diameter in feet would be 2 inches / 12 = 0.1667 ft.
Now, we need to find the radius of the base. The radius is equal to half of the diameter, so the radius is 0.1667 ft / 2 = 0.08335 ft.
Let's substitute the values into the volume formula:
V = (1/3) * π * (0.08335 ft)^2 * 2.1 ft
≈ (1/3) * 3.14159 * (0.0069495 ft^2) * 2.1 ft
≈ 0.0219177 ft^3
When rounded to three decimal places, the volume of the cone is approximately 0.022 ft^3. None of the given answer choices match this result exactly, but the closest option is 0.061 ft^3. However, it may be worth checking if there was a mistake in the provided answer choices or if any rounding errors occurred during the calculation.