A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is 24 square centimeters. What is the height, in centimeters, of the cylinder?
Correct answer: A. 18
- A. 18
- B. 24
- C. 216
- D. 10,368
Explanation
Choice A is correct. The volume V of a right circular cylinder is calculated using the formula V = πr^2h, where πr^2 is the area of the base of the cylinder and h is the height. Given a volume of 432 cubic centimeters and a base area of 24 square centimeters, substituting these values into the formula yields 432 = 24h. Solving for h, divide both sides by 24 to find h = 18 centimeters. Therefore, the height of the cylinder is 18 centimeters.Choices B, C, and D are incorrect because they result from misunderstandings or miscalculations of either the formula or the given values. Choice B confuses the area of the base with the height. Choices C and D involve incorrect assumptions about the base area, leading to significantly wrong calculations.
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