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Sub 505 (Easy)|   Geometry|      
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Bunuel
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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 25 Feb 2015, 02:58
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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
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D
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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 Updated on: 25 Feb 2015, 16:49
Originally posted by ynaikavde on 25 Feb 2015, 08:19.
Last edited by ynaikavde on 25 Feb 2015, 16:49, edited 1 time in total.
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1:8 can be expressed as 1^3:2^8 which tell us that sides are in the ratio 1:2 and the surface area will be in ration of 1:4 answer D
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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 25 Feb 2015, 11:35
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If the formula is known, this can easily be solved by number picking:

volume: a^3

a of cube 1 = 1

1 * 1 *1 = 1

a of cube 2 = 2

2* 2 * 2 = 8

Ratio 1:8

surface: 6 * a^2

6 * 1 = 6

6* 4 = 24

Ratio: 1:4

Answer D
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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 28 Feb 2015, 06:49
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Bunuel
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


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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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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 02 Mar 2015, 06:21
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Bunuel
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


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MAGOOSH OFFICIAL SOLUTION:
Attachment:
cubesurface_explanation.png
cubesurface_explanation.png [ 43.08 KiB | Viewed 18663 times ]
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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 02 Mar 2015, 06:22
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Bunuel
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


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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 08 Jul 2019, 02:28
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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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If the ratio of the volume of cube A to the volume of cube B is 1 to 8 24 Aug 2022, 15:28
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