Find the height and volume of a cone with slant height of 41 feet and a radius of 40 feet. Use 3.14 for pi.
To find the height of the cone, we can use the Pythagorean theorem.
The slant height (l) is the hypotenuse, the radius (r) is one leg, and the height (h) is the other leg.
Using the formula:
l^2 = r^2 + h^2
41^2 = 40^2 + h^2
1681 = 1600 + h^2
81 = h^2
h = 9 feet
Now that we have found the height of the cone, we can find the volume using the formula:
Volume = (1/3) * π * r^2 * h
Volume = (1/3) * 3.14 * 40^2 * 9
Volume = (1/3) * 3.14 * 1600 * 9
Volume = (1/3) * 3.14 * 14400
Volume = 15072 cubic feet
Therefore, the height of the cone is 9 feet and the volume of the cone is 15072 cubic feet.