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A piece of cardboard measures 30 cm by 40 cm. We can make tw

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A piece of cardboard measures 30 cm by 40 cm. We can make tw

by Max@Math Revolution » Mon Jul 23, 2018 12:07 am

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[Math Revolution GMAT math practice question]

A piece of cardboard measures 30 cm by 40 cm. We can make two different right circular cylinders by rolling the cardboard along its length and by rolling the cardboard along its width. What is the difference in their volumes?

A. 1000 / π
B. 2000 / π
C. 3000 / π
D. 4000 / π
E. 5000 / π
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by Max@Math Revolution » Tue Jul 24, 2018 11:31 pm
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Case 1: 2Ï€r = 30 and h = 40
r = 15/Ï€
The volume is πr^2*h = π(15/π)^2 * 40 = ( 225 * 40 ) / π = 9000 / π.

Case 2: 2Ï€r = 40 and h = 30
r = 20/Ï€
The volume is πr^2*h = π(20/π)^2 * 30 = ( 400 * 30 ) / π = 12000 / π.

Thus, the difference in the two volumes is 12000 / π - 9000 / π = 3000 / π.


Therefore, C is the answer.
Answer: C
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by swerve » Wed Jul 25, 2018 9:33 am
If the cylinder is rolled along 30...
Circumference of circle so formed = 2Ï€r=30..... r=15/Ï€
Height =40
$$V=\pi\cdot\frac{15^2}{\pi}\cdot40$$
For the other volume 30 and 40 will interchange
So $$V=\pi\cdot\frac{20^2}{\pi}\cdot30$$
Difference = (20^2*30-15^2*40)/π = (12000-9000)/ π = 3000/π.

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by Jeff@TargetTestPrep » Thu Jul 26, 2018 3:24 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

A piece of cardboard measures 30 cm by 40 cm. We can make two different right circular cylinders by rolling the cardboard along its length and by rolling the cardboard along its width. What is the difference in their volumes?

A. 1000 / π
B. 2000 / π
C. 3000 / π
D. 4000 / π
E. 5000 / π
If we roll the cardboard along its length, we will have the circumference of the circular base of the cylinder = 40 cm and the height of the cylinder = 30 cm. In this case, we have radius = 40/2π = 20/π and the volume = π r^2 h = π x (20/π)^2 x 30 = π x 400/π^2 x 30 = 12,000/π.

Similarly, if we roll the cardboard along its width, we will have the circumference of the circular base of the cylinder = 30 cm and the height of the cylinder = 40 cm. In this case, we have radius = 30/2π = 15/π and the volume = π r^2 h = π x (15/π)^2 x 40 = π x 225/π^2 x 40 = 9,000/π.

Thus, the difference between the two volumes is 12,000/Ï€ - 9,000/Ï€ = 3,000/Ï€.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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