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505-555 (Easy)|   Geometry|      
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If the volume of a cube is v, what is the surface area of the cube in 26 Jun 2018, 20:56
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E
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88% (00:56) correct 13% (00:51) wrong based on 67 sessions

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If the volume of a cube is v, what is the surface area of the cube in terms of v?


A. \(6 \sqrt{V}\)

B. \((\sqrt{V})^3\)

C. \(6 * (\sqrt{V})^3\)

D. \((\sqrt[3]{V})^2\)

E. \(6 * (\sqrt[3]{V})^2\)
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E
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If the volume of a cube is v, what is the surface area of the cube in 26 Jun 2018, 21:48
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The volume of cube = \(a^3\), where a is the side of cube
Thus \(a^3\) = V.
hence \(a= V^1/3\).
Surface area(S.A)= \(6 a^2\).
Thus S.A = \(6∗V^(2/3)\)

Ans E
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If the volume of a cube is v, what is the surface area of the cube in 26 Jun 2018, 22:01
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Solution



Given:
    • The volume of a cube is V

To find:
    • The surface area of the cube, in terms of V

Approach and Working:
If we assume the length of each side of the cube is x, then
    • Volume \(V = x^3\)
    Or, \(x = V^\frac{1}{3}\)

    • Surface area of the cube = \(6x^2 = 6 * V^\frac{2}{3}\) = \(6 * (\sqrt[3]{V})^2\)

Hence, the correct answer is option E.

Answer: E
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If the volume of a cube is v, what is the surface area of the cube in 27 Jun 2018, 05:40
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Let's assume Volume of Cube V=a^3 (a is the individual side length of cube)
Therefore, a=V^1/3 ---- 1>
Now, Surface Area of Cube S= 6.a^2
therefore, S= 6.V^2/3 (Substituting from 1)
Choice-E.
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If the volume of a cube is v, what is the surface area of the cube in 27 Jun 2018, 07:03
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Bunuel
If the volume of a cube is v, what is the surface area of the cube in terms of v?


A. \(6 \sqrt{V}\)

B. \((\sqrt{V})^3\)

C. \(6 * (\sqrt{V})^3\)

D. \((\sqrt[3]{V})^2\)

E. \(6 * (\sqrt[3]{V})^2\)
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Alternate approach

Formula used:
Volume of a cube = \(a^3\) | Surface area of a cube = \(6a^2\) where \(a\) is the side of a cube

Let's assume the value of the volume of the cube to be 8
If the volume of the cube is 8, the side is \((\sqrt[3]{8}) = 2\), the surface area is \(6*2^2 = 24\)

Evaluating answer options with \(V = 8\)

A. \(6 \sqrt{V} = 6 \sqrt{8} = 12\sqrt{2}\)
B. \((\sqrt{V})^3 = (\sqrt{8})^3 = 16\sqrt{2}\)
C. \(6 * (\sqrt{V})^3 = 6 * (\sqrt{8})^3 = 96\sqrt{2}\)
D. \((\sqrt[3]{V})^2 = (\sqrt[3]{8})^2 = 4\)
E. \(6 * (\sqrt[3]{V})^2 = 6 * (\sqrt[3]{8})^2 = 6*4 = 24\) (Option E)
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If the volume of a cube is v, what is the surface area of the cube in 02 Jul 2018, 10:05
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Bunuel
If the volume of a cube is v, what is the surface area of the cube in terms of v?


A. \(6 \sqrt{V}\)

B. \((\sqrt{V})^3\)

C. \(6 * (\sqrt{V})^3\)

D. \((\sqrt[3]{V})^2\)

E. \(6 * (\sqrt[3]{V})^2\)
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Since volume of a cube is V = s^3, we have:

s^3 = V

s = ∛V

Since the surface area of a cube is A = 6s^2, we have:

A = 6(∛V)^2

Answer: E
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