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Area and volume SAT question

Math · Geometry and Trigonometry · Hard · Answer it here, explanation included.

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 ?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

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 .

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