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Geometry and Trigonometry / Area and volume Difficulty: Hard

A right circular cone has a height of $22 centimeters left parenthesis cm right parenthesis$ and a base with a diameter of $6 cm$ . The volume of this cone is $n π {cm}^{3}$ . What is the value of $n$ ?

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Explanation

The correct answer is $66$ . It’s given that the right circular cone has a height of $22$ centimeters $(cm)$ and a base with a diameter of $6 cm$ . Since the diameter of the base of the cone is $6 cm$ , the radius of the base is $3 cm$ . The volume $V$ , $in {cm}^{3}$ , of a right circular cone can be found using the formula $V = \frac{1}{3} π r^{2} h$ , where $h$ is the height, $in cm$ , and $r$ is the radius, $in cm$ , of the base of the cone. Substituting $22$ for $h$ and $3$ for $r$ in this formula yields $upper V equals one third pi left parenthesis 3 right parenthesis squared left parenthesis 22 right parenthesis$ , or $upper V equals 66 pi$ . Therefore, the volume of the cone is $66 pi italic cm cubed$ . It’s given that the volume of the cone is $n π {cm}^{3}$ . Therefore, the value of $n$ is $66$ .