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vaibhav1221
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Schools: IIMA '25 (A) Columbia CBS'26 (D) Fuqua '26 (D) ISB '25 (WL) Darden '26 (D) Kenan-Flagler '26 (WL)
GMAT 1: 710 Q49 V38
Posts: 292
Updated on: 23 Jan 2022, 04:26
Originally posted by vaibhav1221 on 22 Jan 2022, 01:15.
Last edited by Bunuel on 23 Jan 2022, 04:26, edited 3 times in total.
Last edited by Bunuel on 23 Jan 2022, 04:26, edited 3 times in total.
Edited the question.
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Difficulty:
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31% (02:23) correct
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A cone has been divided into four slices parallel to the base. The heights of the various slices from top to bottom are in the ratio 1 : 2 : 3 : 4. If the volume of the bottommost slice is 784 cm^3, what is difference in volumes of the third slice from the top and the second slice from the top (in cm^3)?
A. 576
B. 196
C. 729
D. 125
E. 163
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Question.png [ 8.49 KiB | Viewed 3855 times ]
12 Feb 2022, 05:49
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There is only one concept we need to know here - the rest if just plain arithmetic/algebra. The ratio of volumes of two similar bodies is proportional to the ratio of the cubes of their corresponding sides.
Let's assume the volumes are 1V, 27V, 216V and 1000V. We are given that the fourth slice = 784 cm^3. So, 1000V - 216V = 784. Therefore, we get V = 1 cm^3.
Plugging the values, we get volume of third slice = 216V - 27V = 189 (We need to subtract the volume of the preceding cone to get the volume of a given slice)
volume of second slice = 27V - 1V = 26
So, the difference in volumes = 189 - 26 = E) 163
cc: [b]Bunuel, vaibhav1221
- Ratio of heights of the four segments = 1:2:3:4
Ratio of heights of the four cones (from the top) = 1:3:6:10 (Add the heights of the previous segments)
Then, the corresponding ratios of their volumes will be: 1^3:3^3:6^3:10^3, i.e. 1:27:216:1000
Let's assume the volumes are 1V, 27V, 216V and 1000V. We are given that the fourth slice = 784 cm^3. So, 1000V - 216V = 784. Therefore, we get V = 1 cm^3.
Plugging the values, we get volume of third slice = 216V - 27V = 189 (We need to subtract the volume of the preceding cone to get the volume of a given slice)
volume of second slice = 27V - 1V = 26
So, the difference in volumes = 189 - 26 = E) 163
cc: [b]Bunuel, vaibhav1221
