The volume of a cone is three hundred cubic kilometers. If the radius of the base is 9 kilometers, what is the height of the cone? Use three point one four for pi. Show your work and round to the nearest tenth.
The formula for the volume of a cone is
V = (1/3)*pi*R^2*H
In this case, invert the formula and solve for H, the height.
You should do your own calculations.
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To find the height of the cone, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
where V is the volume, π is approximately 3.14, r is the radius of the base, and h is the height of the cone.
Given that the volume of the cone is 300 cubic kilometers, the radius is 9 kilometers, and using π as 3.14, we can rearrange the formula to solve for h:
300 = (1/3) * 3.14 * 9^2 * h
First, let's calculate the value of 9^2:
9^2 = 81
Now, substitute the values back into the formula:
300 = (1/3) * 3.14 * 81 * h
Simplify further:
300 = (0.3333) * 3.14 * 81 * h
300 ≈ 0.1047 * 81 * h
Next, divide both sides of the equation by 0.1047 * 81 to isolate h:
h ≈ 300 / (0.1047 * 81)
h ≈ 1073.598
Rounding to the nearest tenth:
h ≈ 1073.6 kilometers
Therefore, the height of the cone is approximately 1073.6 kilometers.