一个ll ACT Math Resources
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.
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 #31 :Solid Geometry
一个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?
If we letrepresent 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 ofis 27 times as large as the small cube's volume of.
Example Question #2 :How To Find The Volume Of A Cube
一个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?
Example Question #1 :How To Find The Volume Of A Cube
What is the volume of a cube that has a side length ofinches?
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 #1 :How To Find The Volume Of A Cube
What is the volume of a cube with a side of length 1 cm?
The formula for the volume of a cube with a side of lengthis:
Example Question #3 :How To Find The Volume Of A Cube
一个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?
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 #2 :How To Find The Volume Of A Cube
Find the volume of a cube with side length 10.
To find volume, simply cube the side length. Thus,
Example Question #31 :Cubes
Find the volume of a cube whose side length is 0.1.
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 #32 :Cubes
Find the volume of a cube given side length is.
To solve, simply cube the side length. Thus,
Example Question #1 :How To Find The Length Of An Edge Of A Pyramid
一个square pyramid has a volume ofand a height of. What is the perimeter of the base of the pyramid?
The formula for the volume of a pyramid is:
We know thatand; 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 thatandare the same. Therefore, we can substitutefor, 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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