# How do you get the volume of a shape

Find the length of one side of the cube. Measure the object if the radius is not given. Calculate the area of the circular base.

Area is expressed in square units, because it is two measurements multiplied together. Volume is expressed in cubic units, because it is the sum of three measurements length, width and depth multiplied together.

Cubic units include cm 3m 3 and cubic feet. It is therefore best to stick to either liquid or solid volume units. For more, see our page on Systems of Measurement. How you refer to the different dimensions does not change the calculation: The important thing is that the three dimensions are multiplied together.

You can multiply in which ever order you like as it won't change the answer see our page on multiplication for more. This basic formula can be extended to cover the volume of cylinders and prisms too. Instead of a rectangular end, you simply have another shape: Milliliters, liters, gallons are also used especially when measuring liquids. Calculating the volume of a cylinder involves multiplying the area of the base by the height of the cylinder. The base of a cylinder is circular and the formula for the area of a circle is: There is more here on the area of a circle.

The volume of a cone is equal to one-third the volume of a cylinder with matching height and area of base. This gives the formula for the volume of a cone as shown below. You will get other geometry worksheets on perimeter, area, and more here.

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The width of the rectangular solid is the measurement of the shorter side of the solid, parallel to the ground or surface the shape is resting on. Again, look for a label on the diagram indicating the width, or measure your shape with a ruler or tape measure.

#### Calculating Volume

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! Find the height of the rectangular solid.

This height is the distance from the ground or surface the rectangular solid is resting on to the top of the rectangular solid. Locate the information in your diagram, or measure the height using a ruler or tape measure. Plug the dimensions of the rectangular solid into the volume formula and calculate.

Be sure to express your answer in cubic units. Since our example rectangle was measured in inches, the volume should be written as 72 cubic inches, or 72 in 3. If the measurements of our rectangular solid were: Learn to identify a cylinder. A cylinder is a three-dimensional shape that has two identical flat ends that are circular in shape, and a single curved side that connects them.

Memorize the formula for the volume of a cylinder. To calculate the volume of a cylinder, you must know its height and the radius of the circular base the distance from the center of the circle to its edge at the top and bottom. 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. 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: Find the radius of the base. If it is given in the diagram, simply use that number.

Measure the object if the radius is not given. Be aware that getting precise measurement of a circular solid can be a bit tricky.

Math Antics - VolumeOne option is to measure the base of the cylinder across the top with a ruler or tape measure. Do your best to measure the width of the cylinder at its widest part, and divide that measurement by 2 to find the radius.

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: For example, if the circumference you measured was 8 inches, the radius would be 1.

## How to Calculate the Volume

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. Calculate the area of the circular base.

You simply need to divide the diameter in half to find the radius. Find the height of the cylinder. This is simply the distance between the two circular bases, or the distance from the surface the cylinder is resting on to its top.

### 3D Shapes and Volume

Find the label in your diagram that indicates the height of the cylinder, or measure the height with a ruler or tape measure. Multiply the area of the base times the height of the cylinder to find the volume. For our example cylinder with radius 4 inches and height 10 inches: Remember to state your answer in cubic units. Our example cylinder was measured in inches, so the volume must be expressed in cubic inches: If our cylinder had been measured in centimeters, the volume would be expressed in cubic centimeters cm 3.

Understand what a regular pyramid is. Find the volume of this cylinder. Plug in the numbers: Example math problems related to pyramids: Find the volume of this square pyramid. Find the volume of this triangular pyramid.

Find the volume of this cone.