ACT Math : Solid Geometry

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #41 : Solid Geometry

Chemicals to clean a swimming pool cost $0.24 per cubic foot of water. If a pool is 6 feet deep, 14 feet long and 8 feet wide, how much does it cost to clean the pool? Round to the nearest dollar.

 

Possible Answers:

Correct answer:

Explanation:

The volume of the pool can be determined by multiplying the length, width, and height together.  

Each cubit foot costs 24 cents, so:

Example Question #1 : How To Find The Volume Of A Cube

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

Possible Answers:

Correct answer:

Explanation:

If we let  represent the length of an edge on the smaller cube, its volume is .

The larger cube has edges three times as long, so the length can be represented as . The volume is , which is .

The large cube's volume of  is 27 times as large as the small cube's volume of .

 

Example Question #16 : How To Find The Volume Of A Cube

A tank measuring 3in wide by 5in deep is 10in tall.  If there are two cubes with 2in sides in the tank, how much water is needed to fill it?

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Find The Volume Of A Cube

What is the volume of a cube that has a side length of  inches?

Possible Answers:

Correct answer:

Explanation:

We are given the side length of a cube so we simply plug that into the formula for the volume of a cube.

That formula is , and so the correct answer is 

.

Make sure to check your units,  is the correct number, but the units are squared rather than cubed.

Example Question #2 : How To Find The Volume Of A Cube

What is the volume of a cube with a side of length 1 cm?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a cube with a side of length  is:

Example Question #3 : How To Find The Volume Of A Cube

A cube of sponge has volume . When water is added, the sponge triples in length along each dimension. What is the new volume of the cube, in cubic centimeters?

Possible Answers:

Correct answer:

Explanation:

If our original cube has a volume of , then the length of one of its edges is . Triple each edge to , then cube the result, and we obtain 

Example Question #4 : How To Find The Volume Of A Cube

Find the volume of a cube with side length 10.

Possible Answers:

Correct answer:

Explanation:

To find volume, simply cube the side length. Thus,

Example Question #41 : Solid Geometry

Find the volume of a cube whose side length is 0.1.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for volume of a cube. The volume of a cube is length times width times height. Since the height, width, and length are equal on a cube the formula becomes side cubed.

We are given the side length of 0.1 thus,

Example Question #42 : Solid Geometry

Find the volume of a cube given side length is .

Possible Answers:

Correct answer:

Explanation:

To solve, simply cube the side length. Thus,

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

A square pyramid has a volume of  and a height of . What is the perimeter of the base of the pyramid?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a pyramid is:

We know that  and ; however, this still leaves us with two variables in the equation:  and . By definition, a square pyramid's base has sides of equal length, meaning that  and  are the same. Therefore, we can substitute  for , or .

This gives us a new equation of:

We then plug in the variables we know:

Multiply both sides by 3:

Divide both sides by 9:

Therefore, we now know that the length of the pyramid's base is . The question, however, asks for the perimeter of the pyramid's base. Since all of the sides of the base are the same, they must all be . So we multiply . Therefore, the perimeter of the pyramid's base is .

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