Answer:
b. 75.4 m³
Explanation:
You want the volume of the oblique cone with height 8 m and slant height 10 m where the 8 m edge of the cone is perpendicular to one edge of the base.
Diameter
The drawing shows the diameter of the base of the cone is one leg of a right triangle with the other leg 8 m and hypotenuse 10 m. This ratio of 8:10 = 4:5 between the leg and the hypotenuse tells you the right triangle is a 3:4:5 right triangle, scaled by a factor of 2 m.
The diameter of the cone is (2m)·3 = 6 m, so the radius is 3 m.
Volume
The volume formula is ...
V = 1/3πr²h
V = 1/3(3.14)(3 m)²(8 m) = 75.4 m³
The volume of the cone is about 75.4 cubic meters.
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Additional comment
You can solve the triangle for the missing leg length using the Pythagorean theorem:
d² + 8² = 10²
d = √(100 -64) = √36 = 6 . . . . . diameter of the base
The formula for the volume of the cone works for any cone that has circular cross sections that decrease in diameter linearly with the height from the base to the peak.
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