sat suite question viewer

Geometry and Trigonometry / Area and volume Difficulty: Medium

A right circular cylinder has a volume of $45 pi$ . If the height of the cylinder is 5, what is the radius of the cylinder?

Back question 1 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 of a right circular cylinder with a radius of r is the product of the area of the base, $pi, r squared$ , and the height, h. The volume of the right circular cylinder described is $45 pi$ and its height is 5. If the radius is r, it follows that $45 pi equals, pi times, r, squared, times 5$ . Dividing both sides of this equation by $5 pi$ yields $9 equals r squared$ . Taking the square root of both sides yields $r equals 3$ or $r equals negative 3$ . Since r represents the radius, the value must be positive. Therefore, the radius is 3.

Choice B is incorrect and may result from finding that the square of the radius is 9, but then from dividing 9 by 2, rather than taking the square root of 9. Choice C is incorrect. This represents the square of the radius. Choice D is incorrect and may result from solving the equation $45 pi equals, pi times, r, squared, times 5$ for $r squared$ , not r, by dividing by $pi$ on both sides and then by subtracting, not dividing, 5 from both sides.