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Geometry and Trigonometry / Area and volume Difficulty: Medium

A right circular cylinder has a volume of $377$ cubic centimeters. The area of the base of the cylinder is $13$ square centimeters. What is the height, in centimeters, of the cylinder?

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Explanation

The correct answer is $29$ . The volume, $V$ , of a right circular cylinder is given by the formula $V = π r^{2} h$ , where $r$ is the radius of the base of the cylinder and $h$ is the height of the cylinder. Since the base of the cylinder is a circle with radius $r$ , the area of the base of the cylinder is $π r^{2}$ . It's given that a right circular cylinder has a volume of $377$ cubic centimeters; therefore, $upper V equals 377$ . It's also given that the area of the base of the cylinder is $13$ square centimeters; therefore, $pi r squared equals 13$ . Substituting $377$ for $V$ and $13$ for $π r^{2}$ in the formula $V = π r^{2} h$ yields $377 equals 13 h$ . Dividing both sides of this equation by $13$ yields $29 equals h$ . Therefore, the height of the cylinder, in centimeters, is $29$ .