sat suite question viewer

Geometry and Trigonometry / Area and volume Difficulty: Medium

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?

Back question 60 of 86 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

Explanation

Choice A is correct. The volume, $V$ , of a right circular cylinder is given by the formula $V = π r^{2} h$ , where $π r^{2}$ is the area of the base of the cylinder and $h$ is the height. It’s given that a right circular cylinder has a volume of $432$ cubic centimeters and the area of the base is $24$ square centimeters. Substituting $432$ for $V$ and $24$ for $π r^{2}$ in the formula $V = π r^{2} h$ yields $432 equals 24 h$ . Dividing both sides of this equation by $24$ yields $18 equals h$ . Therefore, the height of the cylinder, in centimeters, is $18$ .

Choice B is incorrect. This is the area of the base, in square centimeters, not the height, in centimeters, of the cylinder.

Choice C is incorrect. This is the height, in centimeters, of a cylinder if its volume is $432$ cubic centimeters and the area of its base is $2$ , not $24$ , cubic centimeters.

Choice D is incorrect. This is the height, in centimeters, of a cylinder if its volume is $432$ cubic centimeters and the area of its base is $\frac{1}{24}$ , not $24$ , cubic centimeters.