GMAT Math : Calculating the length of an edge of a cube

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Example Questions

Example Question #1 : Cubes

If the volume of a cube is units cubed, what is the length of each side of the cube?

Possible Answers:

Correct answer:

Explanation:

We solve for the side of the cube by deriving it from the volume of a cube formula:

V=s^3

$s=\sqrt[3]{V}$

$s=\sqrt[3]{27}$

s=3

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Example Question #2 : Cubes

If a cube has a surface area of 54cm^2 , what is the length of one side?

Possible Answers:

9 cm

3 in

3 cm

15 in

6 cm

Correct answer:

3 cm

Explanation:

To find the surface area of a cube, use the following formula:

SA=6s^2

Where s is our side length.

Rearrange for s to get the following:

$s=\sqrt{\frac{SA}{6}}$

Plug in 54 for SA and solve

$s=\sqrt{\frac{54}{6}}=\sqrt{9}=3$

Don't forget your units, in this case centimeters so we get 3 centimeters

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Example Question #3 : Calculating The Length Of An Edge Of A Cube

If a cube has a surface area of 216 , what is the length of one of its sides?

Possible Answers:

Correct answer:

Explanation:

To solve for the side length of the cube, we need to use the formula for surface area. There are six faces on a cube, so its total surface area is just six times the area of one of its square faces, which is given by the side length squared:

SA=6L^2

216=6L^2

$L^2=\frac{216}{6}=36$

$L=\sqrt{36}=6$

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Example Question #4 : Calculating The Length Of An Edge Of A Cube

If a cube has a volume of 343 cm^3 and is made up of smaller cubes, what is the length of one side of one of the smaller cubes?

Possible Answers:

$\small \small \frac{3}{7}cm$

$\small 7 cm$

$\small 3cm$

$\small \frac{7}{3}cm$

Correct answer:

$\small \frac{7}{3}cm$

Explanation:

Volume of a cube is equal to the cube of its side. 343 is equal to 7 cubed, so the length of the whole cube is 7 cm. The cube is made up of 27 smaller cubes though. That means that one face of the cube is made up of 9 cubes and one edge of the whole cube is made up of 3 small cubes. That means that the length of one small cube is equal to the total length of one side divided by the numbers of cubes per side

$\small V=s^3$

$\small \sqrt[3]{343}=7$

Then we get our final answer by doing:

$\small \frac{7}{3}cm$

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Example Question #5 : Calculating The Length Of An Edge Of A Cube

ABCDEFGH is a cube with diagonal HB=3 . What is the length of an edge of the cube?

Possible Answers:

$\sqrt{2}$

$3\sqrt{2}$

$2\sqrt{2}$

$\sqrt{3}$

Correct answer:

$\sqrt{3}$

Explanation:

We are given the length of the diagonal of the cube.

Therefore we can find the length of an edge by using the formula

$d=e\sqrt{3}$ or $e=\frac{d}{\sqrt{3}}$ , and $\frac{3}{\sqrt{3}}=\frac{3}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=\sqrt{3}$ .

Therefore, the final answer is $\sqrt{3}$ .

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Example Question #3 : Cubes

Find the length of the edge of a cube given that the volume is .

Possible Answers:

Correct answer:

Explanation:

To find side length, you must use the equation for volume of a cube and solve for .

$V=s^3\Rightarrow s=\sqrt[3]{V}$

Thus,

$s=\sqrt[3]{64}=4$

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GMAT Math : Calculating the length of an edge of a cube

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Cubes

Example Question #2 : Cubes

Example Question #3 : Calculating The Length Of An Edge Of A Cube

Example Question #4 : Calculating The Length Of An Edge Of A Cube

Example Question #5 : Calculating The Length Of An Edge Of A Cube

Example Question #3 : Cubes

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