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Re: If the ratio of the volume of cube A to the volume of cube B is 1 to 8 [#permalink]
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Bunuel wrote:
If the ratio of the volume of cube A to the volume of cube B is 1 to 8, what is the ratio of the surface area of cube A to the surface area of cube B?

A. \(1:\sqrt{2}\)
B. 1:2
C. \(1:2\sqrt{2}\)
D. 1:4
E. 1:8


Kudos for a correct solution.


Volume of cube = a^3
Surface area of cube = 6a^2

Given that, Va/Vb = 1/8
So, A^3/B^3 = 1/8
So, A/B = 1/2

Ratio of surface areas of cube = (6A^2)/(6B^2)
= A^2/B^2
= (A/B)^2
= (1/2)^2
= 1/4
Hence option D.
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Re: If the ratio of the volume of cube A to the volume of cube B is 1 to 8 [#permalink]
Expert Reply
Bunuel wrote:
If the ratio of the volume of cube A to the volume of cube B is 1 to 8, what is the ratio of the surface area of cube A to the surface area of cube B?

A. \(1:\sqrt{2}\)
B. 1:2
C. \(1:2\sqrt{2}\)
D. 1:4
E. 1:8


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
cubesurface_explanation.png
cubesurface_explanation.png [ 43.08 KiB | Viewed 17001 times ]
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Re: If the ratio of the volume of cube A to the volume of cube B is 1 to 8 [#permalink]
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Expert Reply
Bunuel wrote:
If the ratio of the volume of cube A to the volume of cube B is 1 to 8, what is the ratio of the surface area of cube A to the surface area of cube B?

A. \(1:\sqrt{2}\)
B. 1:2
C. \(1:2\sqrt{2}\)
D. 1:4
E. 1:8


Kudos for a correct solution.


Check other 3-D Geometry Questions in our Special Questions Directory.
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Re: If the ratio of the volume of cube A to the volume of cube B is 1 to 8 [#permalink]
From given information
Volume of A cube = 1 that mean its length and width is same so the area of cube A is 1 and the cube a has 6 faces that why i need to multiply the area with 6 faces
So surface area = 1X6 = 6
In the same way i easily calculate the surface area of B cube
B cube = 2cube3
b=2
area = 2x2
=4
surface area = 4x6
=24
Surface area of cube A: surface area of cube B
6:24
1:4
Answer is 1:4
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Re: If the ratio of the volume of cube A to the volume of cube B is 1 to 8 [#permalink]
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Re: If the ratio of the volume of cube A to the volume of cube B is 1 to 8 [#permalink]
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