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17 Sep 2018, 21:57
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47%
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The ratio of the volume of cube A to the volume of cube B is 1 to \(3\sqrt{3}\). If the diagonal of cube A is 10, what is the area of a face of cube B?
A. 10
B. 100/3
C. \(30\sqrt{3}\)
D. 100
E. \(300\sqrt{3}\)
A. 10
B. 100/3
C. \(30\sqrt{3}\)
D. 100
E. \(300\sqrt{3}\)
18 Sep 2018, 01:15
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Bunuel
The ratio of the volume of cube A to the volume of cube B is 1 to \(3\sqrt{3}\). If the diagonal of cube A is 10, what is the area of a face of cube B?
A. 10
B. 100/3
C. \(30\sqrt{3}\)
D. 100
E. \(300\sqrt{3}\)
A. 10
B. 100/3
C. \(30\sqrt{3}\)
D. 100
E. \(300\sqrt{3}\)
Ratio of Volume = (Ratio of Sides)^3
Given, Ratio of Volumes of A and B = 1/3√3 = 1/√27 = (Ratio of Sides)^3
i.e. Ratio of Sides = 1/√3
i.e. Diagonal of cube A / Diagonal of Cube B = 1/√3
i.e. Diagonal of Cube B = 10√3 = Side√3
i.e. Side of Cube B = 10
i.e. Area of face of Cube B = 10^2 = 100
Answer:option D
18 Sep 2018, 03:14
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Bunuel
The ratio of the volume of cube A to the volume of cube B is 1 to \(3\sqrt{3}\). If the diagonal of cube A is 10, what is the area of a face of cube B?
A. 10
B. 100/3
C. \(30\sqrt{3}\)
D. 100
E. \(300\sqrt{3}\)
A. 10
B. 100/3
C. \(30\sqrt{3}\)
D. 100
E. \(300\sqrt{3}\)
VA:VB = 1: 3\sqrt{3}
let cube A & B have sides a & b resp.
=> \sqrt{3}a = 10
=> a = 10/\sqrt{3}
=> VA = 1000/(\sqrt{3})^3
Since VA:VB = 1:3\sqrt{3} , multiply by 1000/(\sqrt{3})^3
VB becomes 1000
=> b = 10
hence, surface area = 10*10 = 100
