Question

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.

Answer 1

To find the height of the cone, we can use the Pythagorean theorem.

The slant height (l) of the cone, the radius (r) and the height (h) form a right angled triangle.
Using Pythagoras' theorem:
l^2 = r^2 + h^2
41^2 = 40^2 + h^2
1681 = 1600 + h^2
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 use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h

V = (1/3) * 3.14 * 40^2 * 9
V = (1/3) * 3.14 * 1600 * 9
V = (1/3) * 3.14 * 14400
V = (3.14) * 4800
V = 15072 cubic feet

Therefore, the volume of the cone is 15072 cubic feet.