The roof of a castle is in the shape of a cone. It has a height of 12 feet and a diameter of 6 feet, how much air occupies the roof? (use π = 3.14)
Question
The roof of a castle is in the shape of a cone. It has a height of 12 feet and a diameter of 6 feet, how much air occupies the roof? (use π = 3.14)
Solution
To find the volume of a cone, we use the formula: V = 1/3 * π * r² * h
Given:
- The diameter of the cone (d) is 6 feet, so the radius (r) is d/2 = 6/2 = 3 feet.
- The height (h) of the cone is 12 feet.
- π is approximately 3.14.
Substituting these values into the formula, we get:
V = 1/3 * 3.14 * (3)² * 12 V = 1/3 * 3.14 * 9 * 12 V = 1/3 * 3.14 * 108 V = 113.04 cubic feet.
So, the roof of the castle occupies 113.04 cubic feet of air.
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