Find the volume of a cone with slant height of
265 feet and a radius of 23 feet.
Use 3.14 for π. (The cone is not drawn to scale.)
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, where the slant height (l) is the hypotenuse, the radius (r) is one of the legs, and the height (h) is the other leg.
Using the Pythagorean theorem:
l^2 = r^2 + h^2
(265)^2 = (23)^2 + h^2
265^2 = 529 + h^2
265^2 - 529 = h^2
h = √(265^2 - 529)
h = √(70225 - 529)
h = √69696
h ≈ 264 feet
Therefore, the height of the cone is approximately 264 feet.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Plugging in the values:
V = (1/3) * 3.14 * (23^2) * 264
V = (1/3) * 3.14 * 529 * 264
V = (1/3) * 3.14 * 139656
V = (1/3) * 439101.84
V ≈ 146367.28 cubic feet
Therefore, the volume of the cone is approximately 146367.28 cubic feet.