All ACT Math Resources
Example Questions
Example Question #23 : Cubes
What is the sum of the number of vertices, edges, and faces of a cube?
24
26
20
18
None of the answers are correct
26
Vertices = three planes coming together at a point = 8
Edges = two planes coming together to form a line = 12
Faces = one plane as the surface of the solid = 6
Vertices + Edges + Faces = 8 + 12 + 6 = 26
Example Question #11 : How To Find The Volume Of A Cube
What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14
6.73x3
4.18x3
3.82x3
5.28x3
8.00x3
3.82x3
Vcube = s3 = (2x)3 = 8x3
Vsphere = 4/3 πr3 = 4/3•3.14•x3 = 4.18x3
Example Question #1 : How To Find The Volume Of A Cube
The density of gold is and the density of glass is . You have a gold cube that is in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?
Weight = Density * Volume
Volume of Gold Cube = side3= x3
Weight of Gold = 16 g/cm3 * x3
Weight of Glass = 3/cm3 * side3
Set the weight of the gold equal to the weight of the glass and solve for the side length:
16* x3 = 2 * side3
side3 = 16/2* x3 = 8 x3
Take the cube root of both sides:
side = 2x
Example Question #2 : How To Find The Volume Of A Cube
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 #3 : 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?
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 #43 : Solid Geometry
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?
Example Question #3 : How To Find The Volume Of A Cube
What is the volume of a cube that has a side length of inches?
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 #3 : 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 length is:
Example Question #8 : 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?
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 #9 : 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,