sat suite question viewer

Geometry and Trigonometry / Area and volume Difficulty: Easy

Each base of a right rectangular prism has a length of $19$ inches and a width of $8$ inches. The prism has a volume of $2,736$ cubic inches. What is the height, in inches, of the prism?

Back question 81 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 rectangular prism is given by the formula $V = l w h$ , where $l$ is the length of the base, $w$ is the width of the base, and $h$ is the height of the prism. It’s given that each base of a right rectangular prism has a length of $19$ inches and a width of $8$ inches, and that the prism has a volume of $2,736$ cubic inches. Substituting $19$ for $l$ , $8$ for $w$ , and $2,736$ for $V$ in the formula $V = l w h$ gives $2,736 equals left parenthesis 19 right parenthesis left parenthesis 8 right parenthesis left parenthesis h right parenthesis$ , or $2,736 equals 152 h$ . Dividing each side of this equation by $152$ yields $18 equals h$ . Therefore, the height, in inches, of the prism is $18$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the area, in square inches, of the base of the prism, not the height, in inches, of the prism.