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

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If the volume of a cube is v, what is the surface area of the cube in  [#permalink]

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26 Jun 2018, 20:56
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82% (00:51) correct 18% (00:24) wrong based on 50 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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Re: If the volume of a cube is v, what is the surface area of the cube in  [#permalink]

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26 Jun 2018, 21:48
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  [#permalink]

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26 Jun 2018, 22:01
1

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.

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If the volume of a cube is v, what is the surface area of the cube in  [#permalink]

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27 Jun 2018, 05:40
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  [#permalink]

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27 Jun 2018, 07:03
Bunuel wrote:
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. $$6 * (\sqrt[3]{V})^2$$

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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Re: If the volume of a cube is v, what is the surface area of the cube in  [#permalink]

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02 Jul 2018, 10:05
Bunuel wrote:
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. $$6 * (\sqrt[3]{V})^2$$

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

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Re: If the volume of a cube is v, what is the surface area of the cube in &nbs [#permalink] 02 Jul 2018, 10:05
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