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The figure above is a cube with edges of length 9. Points C
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25 Nov 2020, 09:21
25 Nov 2020, 09:21
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74% (02:18) correct
25% (02:59) wrong based on 43 sessions
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GRE The figure above is a cube with edges of length 9.jpg [ 18.01 KiB | Viewed 1959 times ]
The figure above is a cube with edges of length 9. Points C and D lie on diagonal AB such that points A, C, D, and B are equally spaced. As shown, a right circular cylindrical hole is cut out of the cube so that segment CD is a diameter of the top of the hole. What is the volume of the resulting figure?
A. \(729-162\)
B. \(729-\frac{81\pi}{2}\)
C. \(729-81\pi\)
D. \(729-9\pi\)
E. \(729\)
Re: The figure above is a cube with edges of length 9. Points C
[#permalink]
03 Dec 2020, 23:50
03 Dec 2020, 23:50
1
Length 9=Diagonal of the cube is 9*2^0.5=Diameter of circle is 1/3*9*2^0.5=3*2^0.5
Radius is then (3*2^0.5)/2
Area is r^2=18/4*pi=9/2*pi
Volume=9*9/2*pi
Which is of course subtracted, and seen in answer B
ALT WAY:
Clearly, the volume will have a pi in it, and will be subtracted, so there goes answers A and E right off the bat.
The only way that it can be D is if the cylinder had a diameter of 1, which you can almost instantly see that the diagonal is not just 6
The only way it can be C is if the cylinder has a diameter of 6, which you can tell pretty quickly is not the case from looking at the diagonal, given that it has a radical in it's simplest form of 9*2^0.5, ie, not 18
Only B remains.
Ways to get caught up:
-Trying to do the math for the first path in your head
-Forgetting 45:45:90 triangles
Radius is then (3*2^0.5)/2
Area is r^2=18/4*pi=9/2*pi
Volume=9*9/2*pi
Which is of course subtracted, and seen in answer B
ALT WAY:
Clearly, the volume will have a pi in it, and will be subtracted, so there goes answers A and E right off the bat.
The only way that it can be D is if the cylinder had a diameter of 1, which you can almost instantly see that the diagonal is not just 6
The only way it can be C is if the cylinder has a diameter of 6, which you can tell pretty quickly is not the case from looking at the diagonal, given that it has a radical in it's simplest form of 9*2^0.5, ie, not 18
Only B remains.
Ways to get caught up:
-Trying to do the math for the first path in your head
-Forgetting 45:45:90 triangles
gmatclubot
Re: The figure above is a cube with edges of length 9. Points C [#permalink]
03 Dec 2020, 23:50
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