A 6-sided die is a good example of a cube you might find in your house. Sugar cubes, and children’s letter blocks are also usually cubes.

To find s3, simply multiply s by itself 3 times: s3 = s * s * s

If you are not 100% sure that your shape is a cube, measure each of the sides to determine if they are equal. If they are not, you will need to use the method below for Calculating the Volume of a Rectangular Solid.

Make sure all of the lengths are in the same unit before multiplying them. [5] X Expert Source Grace Imson, MAMath Instructor, City College of San Francisco Expert Interview. 1 November 2019.

A cube is really just a special rectangular solid in which the sides of all of the rectangles are equal.

Example: The length of this rectangular solid is 4 inches, so l = 4 in. Don’t worry too much about which side is the length, which is the width, etc. As long as you end up with three different measurements, the math will come out the same regardless of how your arrange the terms.

Example: The width of this rectangular solid is 3 inches, so w = 3 in. If you are measuring the rectangular solid with a ruler or tape measure, remember to take and record all measurements in the same units. Don’t measure one side in inches another in centimeters; all measurements must use the same unit!

Example: The height of this rectangular solid is 6 inches, so h = 6 in.

In our example, l = 4, w = 3, and h = 6. Therefore, V = 4 * 3 * 6, or 72.

If the measurements of our rectangular solid were: length = 2 cm, width = 4 cm, and height = 8 cm, the Volume would be 2 cm * 4 cm * 8 cm, or 64cm3.

A can is a good example of a cylinder, so is a AA or AAA battery.

In some geometry problems the answer will be given in terms of pi, but in most cases it is sufficient to round pi to 3. 14. Check with your instructor to find out what she would prefer. The formula for finding the volume of a cylinder is actually very similar to that for a rectangular solid: you are simply multiplying the height of the shape by the surface area of its base. In a rectangular solid, that surface area is l * w, for the cylinder it is πr2, the area of a circle with radius r.

Another option is to measure the circumference of the cylinder (the distance around it) using a tape measure or a length of string that you can mark and then measure with a ruler. Then plug the measurement into the formula: C (circumference) = 2πr. Divide the circumference by 2π (6. 28) and that will give you the radius. For example, if the circumference you measured was 8 inches, the radius would be 1. 27in. If you need a really precise measurement, you might use both methods to make sure that your measurements are similar. If they are not, double check them. The circumference method will usually yield more accurate results.

If the radius of the circle is equal to 4 inches, the area of the base will be A = π42. 42 = 4 * 4, or 16. 16 * π (3. 14) = 50. 24 in2 If the diameter of the base is given instead of the radius, remember that d = 2r. You simply need to divide the diameter in half to find the radius.

V = π4210 π42 = 50. 24 50. 24 * 10 = 502. 4 V = 502. 4

We most commonly imagine a pyramid as having a square base, and sides that taper up to a single point, but the base of a pyramid can actually have 5, 6, or even 100 sides! A pyramid with a circular base is called a cone, which will be discussed in the next method.

The volume formula is the same for right pyramids, in which the apex is directly above the center of the base, and for oblique pyramids, in which the apex is not centered.

The formula for the area of a triangle is: A = 1/2bh, where b is the base of the triangle and h is the height. It is possible to find the area of any regular polygon using the formula A = 1/2pa, where A is the area, p is the perimeter of the shape, and a is the apothem, or distance from the center of the shape to the midpoint of any of its sides. This is a pretty involved calculation that goes beyond the scope of this article, but check out Calculate the Area of a Polygon for some great instructions on how to use it. Or you can make your life easy and search for a Regular Polygon Calculator online. [15] X Research source

If we had a different pyramid, with a pentagonal base with area 26, and height of 8, the volume would be: 1/3 * 26 * 8 = 69. 33.

If the vertex of the cone is directly above the center of the circular base, the cone is called a “right cone”. If it is not directly over the center, the cone is called an “oblique cone. " Fortunately, the formula for calculating the area of a cone is the same whether it is right or oblique.

The πr2 part of the formula refers to the area of the circular base of the cone. The formula for the volume of the cone is thus 1/3bh, just like the formula for the volume of a pyramid in the method above!

In the example in the diagram, the radius of the circular base of the cone is 3 inches. When we plug that into the formula we get: A = π32. 32 = 3 *3, or 0, so A = 9π. A = 28. 27in2

In our example, 141. 35 * 1/3 = 47. 12, the volume of our cone. To restate it, 1/3π325 = 47. 12

For example, if you measure a ball and find its circumference is 18 inches, divide that number by 6. 28 and you will find that the radius is 2. 87in. Measuring a spherical object can be a little tricky, so you might want to take 3 different measurements, and then average them together (add the three measurements together, then divide by 3) to make sure you have the most accurate value possible. For example, if your three circumference measurements were 18 inches, 17. 75 inches, and 18. 2 inches, you would add those three values together (18 + 17. 5 + 18. 2 = 53. 95) and divide that value by 3 (53. 95/3 = 17. 98). Use this average value in your volume calculations.

In our example, 36 * 3. 14 = 113. 09.