What is the diameter of a cone with a height of 10 yards and a volume of 92.4 cubic yards? Round to the nearest whole number.

82.97=r^2???

92.4 = 1/3 pi r^2 (10)

r^2 = 8.8

PS: don't forget you want the diameter

So is it 17.6??

no, r^2 = 8.8

r = 2.97, so diameter is 5.94

To find the diameter of a cone, we first need to find the radius. Once we have the radius, we can calculate the diameter by doubling the radius.

To find the radius of the cone, we need to rearrange the formula for the volume of a cone in terms of the radius:

Volume of a cone = (1/3) * π * r^2 * h

In this case, the height (h) is given as 10 yards, and the volume is given as 92.4 cubic yards. Plugging these values into the formula, we have:

92.4 = (1/3) * π * r^2 * 10

Now, we can isolate the radius (r):

92.4 = (1/3) * π * r^2 * 10
92.4 = (10/3) * π * r^2

To simplify, we can divide both sides of the equation by (10/3) * π:

92.4 / ((10/3) * π) = r^2

Now, we can solve for r by taking the square root of both sides:

sqrt(92.4 / ((10/3) * π)) = r

Using a calculator, we can evaluate this expression to find the approximate value of r:

r ≈ 3.617

Finally, to find the diameter, we multiply the radius by 2:

diameter ≈ 2 * 3.617 ≈ 7.234

Rounding this to the nearest whole number, the diameter of the cone is approximately 7 yards.