Use the image to answer the question.
A cone of radius 8 yards and the height is labeled blank yards. There is a right angle symbol between the lines for the radius and height. The base is shaded.
This cone has a volume of 803.84 yd.3 . Find the height of the cone. Let π=3.14 .
To find the height of the cone, we need to use the formula for the volume of a cone.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, π is approximately 3.14, r is the radius of the base, and h is the height.
In this case, we are given that the radius of the cone is 8 yards and the volume is 803.84 yd^3.
Plugging these values into the formula, we get:
803.84 = (1/3)(3.14)(8^2)h
Simplifying this equation, we have:
803.84 = (1/3)(3.14)(64)h
803.84 = (1/3)(200.96)h
803.84 = 66.98667h
Dividing both sides of the equation by 66.98667, we find:
h = 803.84 / 66.98667
h ≈ 11.999
Round this to the nearest whole number, the height of the cone is approximately 12 yards.