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Updated on: 24 Aug 2025, 06:08
Originally posted by Sajjad1994 on 12 Aug 2025, 08:51.
Last edited by Sajjad1994 on 24 Aug 2025, 06:08, edited 1 time in total.
Last edited by Sajjad1994 on 24 Aug 2025, 06:08, edited 1 time in total.
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In the rectangular solid above, points A, B, C, and D are vertices, AB = 8, and all edges meet at right angles. Which of the following statements, considered individually, is sufficient to determine the volume of the solid?
Indicate all that apply.
A. The solid is a cube.
B. The area of one face of the solid is 64.
C. \(BC = CD = AB.\)
D. \(BD=8\sqrt{2}\) and triangle BCD is isosceles.
E. \(AC = BD.\)
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24 Aug 2025, 06:21
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Official Explanation
(A) is sufficient because if the solid is a cube, the volume can be found by cubing the side length 8. That is, volume would equal 83.
(B) is not sufficient because the face with area 64 might have dimensions of, say, 16 × 4 or 32 × 2, producing solids of varying volumes.
(C) is sufficient because if BC = CD = AB = 8, the volume will equal 8 × 8 × 8 = 83, length times width times height.
(D) is sufficient, because in an isosceles right triangle (45-45-90 triangle), it is possible to determine all three side lengths from knowing just one. The leg lengths always equal the length of the hypotenuse divided by Here, BC and CD would both equal and again we know the length, width, and height of the solid.
(E) is not sufficient, because there is no way to determine the solid’s height. The vertical length BC can be stretched to any height, producing varying volumes, but as long as CD = 8, AC will remain equal to BD as given.
The answer is (A), (C), and (D).
(A) is sufficient because if the solid is a cube, the volume can be found by cubing the side length 8. That is, volume would equal 83.
(B) is not sufficient because the face with area 64 might have dimensions of, say, 16 × 4 or 32 × 2, producing solids of varying volumes.
(C) is sufficient because if BC = CD = AB = 8, the volume will equal 8 × 8 × 8 = 83, length times width times height.
(D) is sufficient, because in an isosceles right triangle (45-45-90 triangle), it is possible to determine all three side lengths from knowing just one. The leg lengths always equal the length of the hypotenuse divided by Here, BC and CD would both equal and again we know the length, width, and height of the solid.
(E) is not sufficient, because there is no way to determine the solid’s height. The vertical length BC can be stretched to any height, producing varying volumes, but as long as CD = 8, AC will remain equal to BD as given.
The answer is (A), (C), and (D).
