ACT Math : How to find the length of an edge of a cube

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Length Of An Edge Of A Cube

Our backyard pool holds 10,000 gallons.  Its average depth is 4 feet deep and it is 10 feet long.  If there are 7.48 gallons in a cubic foot, how wide is the pool? 

Possible Answers:

100 ft  

7.48 ft  

 33  ft   

133 ft  

30 ft  

Correct answer:

 33  ft   

Explanation:

There are 7.48 gallons in cubic foot. Set up a ratio:

1 ft3 / 7.48 gallons = x cubic feet / 10,000 gallons

Pool Volume = 10,000 gallons = 10,000 gallons * (1 ft3/ 7.48 gallons) = 1336.9 ft3

Pool Volume = 4ft x 10 ft x WIDTH = 1336.9 cubic feet

Solve for WIDTH:

4 ft x 10 ft x WIDTH = 1336.9 cubic feet

WIDTH = 1336.9 / (4 x 10) = 33.4 ft

Example Question #1 : Cubes

A cube has a volume of 64cm3. What is the area of one side of the cube?

Possible Answers:

4cm

4cm2

16cm

16cm3

16cm2

Correct answer:

16cm2

Explanation:

The cube has a volume of 64cm3, making the length of one edge 4cm (4 * 4 * 4 = 64).

So the area of one side is 4 * 4 = 16cm2

Example Question #1 : How To Find The Length Of An Edge Of A Cube

A cube as the volume of .

Find the length of a side of this cube.

Possible Answers:

Correct answer:

Explanation:

The formula to find the volume of the cube is

Since we know the volume, we can set up the equation

Example Question #2 : Cubes

A cube has a surface area of , what is the length of the side of the cube? (If necessary, round to the nearest hundredth.)

Possible Answers:

Correct answer:

Explanation:

To find the length of the side of a square given the surface area, use the surface area formula and solve for :

, now divide both sides by 6
, now square root both sides
.

Example Question #3 : Cubes

A certain cubic box when unfolded and laid flat on a table covers exactly  square units of space. What is the width of the box, in units?

Possible Answers:

Correct answer:

Explanation:

To find the length of the edge of a cube from its surface area, remember that , where  is the length of a side.

So, the box is  units long.

Example Question #4 : Cubes

Given the volume of a cube is , find the side length.

Possible Answers:

Correct answer:

Explanation:

To find side length, simply realize that volume is the side length cubed. Thus,

Example Question #5 : Cubes

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

Possible Answers:

Correct answer:

Explanation:

To solve, simply take the cube root of the volume. Thus,

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