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In the rectangular solid depicted above , AC = 6, AE = 8, DE = 5, and
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05 Dec 2022, 03:14
05 Dec 2022, 03:14
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Note: Figure not drawn to scale
In the rectangular solid depicted above , AC = 6, AE = 8, DE = 5, and BC > AB > 2.
Which of the following could be possible values for the volume of the shaded area?
a) 60
b) 70
c) 150
d) 170
e) 180
f) 240
Re: In the rectangular solid depicted above , AC = 6, AE = 8, DE = 5, and
[#permalink]
09 Dec 2022, 04:00
09 Dec 2022, 04:00
Expert Reply
OE
First, find the volume of the entire box, which equals 6 × 8 × 5 = 240. Solve for the volume of the three-dimensional triangular shape on top and subtract it from the total volume to find the volume of the shaded part. The triangular shape has known dimensions of 8 by 5. The third dimension ranges based on the length of BC, with 3 < BC < 4 because BC has to be bigger than AB. Therefore, the triangular shape’s volume falls between one-half of 8 × 5 × 3 = 60 and one-half of 8 × 5 × 4 = 80. The shaded area’s volume falls between 240 − 80 = 160 and 240 − 60 = 180. Only choice (D) works.
First, find the volume of the entire box, which equals 6 × 8 × 5 = 240. Solve for the volume of the three-dimensional triangular shape on top and subtract it from the total volume to find the volume of the shaded part. The triangular shape has known dimensions of 8 by 5. The third dimension ranges based on the length of BC, with 3 < BC < 4 because BC has to be bigger than AB. Therefore, the triangular shape’s volume falls between one-half of 8 × 5 × 3 = 60 and one-half of 8 × 5 × 4 = 80. The shaded area’s volume falls between 240 − 80 = 160 and 240 − 60 = 180. Only choice (D) works.
gmatclubot
Re: In the rectangular solid depicted above , AC = 6, AE = 8, DE = 5, and [#permalink]
09 Dec 2022, 04:00
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