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.
The volume of a cone is given by V = (1/3)*pi*r^2*h.
We're given V and h, so solve for r.
Remember, the diameter is two times the radius.
6884.02....yes?
To find the diameter of the cone, we need to use the formula for the volume of a cone, which is given by:
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 of the cone, and h is the height of the cone.
In this case, we are given the height (h) as 10 yards and the volume (V) as 92.4 cubic yards. We need to find the radius (r).
Rearranging the formula to solve for r, we have:
r = √((3V) / (πh))
= √((3 * 92.4) / (π * 10))
Now, let's plug in the given values and calculate the result.
r = √(277.2 / (3.14159 * 10))
To find the diameter of the cone, we need to multiply the radius by 2:
d = 2 * r
Now, let's substitute the value of r and calculate the diameter:
d = 2 * √(277.2 / (3.14159 * 10))
After evaluating this expression, we get the final answer for the diameter of the cone as a whole number by rounding it to the nearest whole number.