A sphere is a perfectly round three-dimensional object, in which every point on the surface is an equal distance from the center. In other words, a sphere is a ball-shaped object. [1] X Research source A cone is a 3-dimensional solid that has a circular base and a single vertex (the point of the cone). Another way to think of this is that a cone is a special pyramid that has a circular base. [2] X Research source A cube is a three-dimensional shape that has six identical square faces. [3] X Research source A rectangular solid, also known as a rectangular prism, is similar to a cube in that it is a three-dimensional shape with six sides, but in this case, the sides are rectangular instead of square. [4] X Research source 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. [5] X Research source A pyramid is a three-dimensional shape with a polygon for a base, and lateral faces that taper at an apex (the point of the pyramid). A regular pyramid is a pyramid in which the base of the pyramid is a regular polygon, meaning that all of the sides of the polygon are equal in length, and all of the angles are equal in measure. [6] X Research source If your object has an irregular shape, you can use the displacement method to determine volume.

Sphere: V=43πr3,{\displaystyle V={\frac {4}{3}}\pi r^{3},} where r is the radius of the sphere. [7] X Research source Cone: V=13πr2h,{\displaystyle V={\frac {1}{3}}\pi r^{2}h,} where r is the radius of the circular base and h is the height of the cone. [8] X Research source Cube: V=s3,{\displaystyle V=s^{3},} where s is the length of any edge. [9] X Research source Rectangular prism: V=lwh,{\displaystyle V=lwh,} where l is the length of a side of a rectangular face, w is the width of a rectangular face, and h is the height of the prism. [10] X Research source Cylinder: πr2h,{\displaystyle \pi r^{2}h,} where r is the radius of the circular base and h is the height of the cone. [11] X Research source Pyramid: V=13Bh,{\displaystyle V={\frac {1}{3}}Bh,} where B is the area of the base of the pyramid and h is the height of the pyramid. [12] X Research source

The radius of a circle is half of the diameter. Measure the diameter by placing a ruler across the middle of the circle and reading the end of the ruler. Calculate the radius by dividing the diameter by 2. Finding the radius of a sphere requires slightly more effort, but can be done in a number of ways detailed in how to find the radius of a sphere. The length, width, and height of objects can be measured with a ruler starting at one end of the object and recording where it stops on the other end of the object.

Remember to express your answer in cubic units. Whether you are using metric or SI, the unit of volume will always be cubic. Be sure to always add units to the end of your calculation.

This method can also be used to determine the volume of a regular shape.

When you record the starting volume of water, be sure to look at the water at eye level and record the value at the bottom of the meniscus. The meniscus is the curve that the water takes when it comes in contact with another surface. [14] X Research source

If any water overflows when you place the object in the beaker, try again with a larger graduated cylinder or use less water.

For example, if you started with 35 mL of water and ended with 65 mL of water, the volume of your object is 65 – 35 = 30 mL or 30 cm3

Find an accurate scale and place the object on it. Record its mass in your notebook. You can also measure mass with a balance. With your object on one side, place weights of known mass on the other side until both sides of the scale are balanced. The mass of your object is equal to the total mass of the balance weights. It’s important to make sure your object is dry before weighing. This ensures that absorbed water does not affect the accuracy of the weighing. If you’re measuring the mass of the liquid, weigh the empty container first. Fill the container and weigh it again. Then, just subtract the mass of the container from the mass of the liquid.

For example, calculate the density ρ{\displaystyle \rho } of a substance with a volume of 8 cm3 and a mass of 24 g. ρ=MV=24 g8 cm3=3 g cm−3{\displaystyle {\begin{aligned}\rho &={\frac {M}{V}}\&={\frac {24{\rm {\ g}}}{8{\rm {\ cm^{3}}}}}\&=3{\rm {\ g\ cm^{-3}}}\end{aligned}}}