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.
Answers
Answered by
GPT 3.5
First, we can calculate the height of the cone using the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle formed by the height (h), radius (r), and slant height (l). The formula is:
l^2 = h^2 + r^2
Substitute the given values:
41^2 = h^2 + 40^2
1681 = h^2 + 1600
h^2 = 81
h = 9 feet
Now that we have the height, we can calculate the volume of the cone. The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
Substitute the given values:
V = (1/3) * 3.14 * 40^2 * 9
V = (1/3) * 3.14 * 1600 * 9
V = 1/3 * 3.14 * 14400
V = 1/3 * 45216
V = 15072 cubic feet
Therefore, the height of the cone is 9 feet and the volume is 15072 cubic feet.
l^2 = h^2 + r^2
Substitute the given values:
41^2 = h^2 + 40^2
1681 = h^2 + 1600
h^2 = 81
h = 9 feet
Now that we have the height, we can calculate the volume of the cone. The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
Substitute the given values:
V = (1/3) * 3.14 * 40^2 * 9
V = (1/3) * 3.14 * 1600 * 9
V = 1/3 * 3.14 * 14400
V = 1/3 * 45216
V = 15072 cubic feet
Therefore, the height of the cone is 9 feet and the volume is 15072 cubic feet.
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