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.
The height of the cone is ___ feet.
The volume of the cone is ____ cubic feet
To find the height of the cone, we can use the Pythagorean theorem.
The slant height, radius, and height of the cone form a right triangle. The slant height (hypotenuse) is 41 feet and the radius (base of the triangle) is 40 feet. Let's use h to represent the height of the cone.
Using the Pythagorean theorem:
h^2 + 40^2 = 41^2
h^2 + 1600 = 1681
h^2 = 1681 - 1600
h^2 = 81
h = √81
h = 9 feet
Therefore, the height of the cone is 9 feet.
To find the volume of the cone, we can use 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) * 45216
Volume = 15072 cubic feet
Therefore, the volume of the cone is 15072 cubic feet.