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Geometry and Trigonometry
Difficulty: Hard
A right circular cone has a height of and a base with a diameter of . The volume of this cone is . What is the value of ?
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Explanation
The correct answer is . It’s given that the right circular cone has a height of centimeters and a base with a diameter of . Since the diameter of the base of the cone is , the radius of the base is . The volume , , of a right circular cone can be found using the formula , where is the height, , and is the radius, , of the base of the cone. Substituting for and for in this formula yields , or . Therefore, the volume of the cone is . It’s given that the volume of the cone is . Therefore, the value of is .