Volume of solids

How to calculate the volume of solids, such as the cube, the sphere, the cylinder, the pyramid, the cone, the ellipsoid, and the rectangular prism is what you will learn here. 

As a warm up, take a look at the figure below looking like a pencil. How would you calculate the volume of the pencil above?

The volume of solids is a measure of the amount of space inside these figures.

Different figures lead to different computation.

Volume of solids

What important observation you need to make before calculating the volume of the pencil above? First, suppose that the pencil is made up of three different solids: a hemisphere, a cone, and a cylinder.

Therefore, volume of pencil = volume of cone + volume of cylinder + volume of hemisphere.

a. Volume of a cone  = (π×r2×h) / 3

π = 3.14, r  = 1.5 cm, and h = 3 cm

Volume of a cone  = (3.14×1.52×3) / 3

Volume of a cone  = (3.14×2.25×3) / 3

Volume of a cone  = (21.195) / 3

Volume of a cone  = 7.065 cm3

b. Volume of a cylinder = π×r2×h

π = 3.14, r  = 1.5 cm, and h = 6 cm

Volume of a cylinder  = 3.14×1.52×6 

Volume of a cylinder  = 3.14×2.25×6

Volume of a cylinder  = 42.39 cm3

c. Volume of a sphere = (2×π×r3) / 3

π = 3.14 and r  = 1.5 cm

Volume of a sphere = (2×3.14×1.53) / 3

Volume of a sphere = (6.28×1.53) / 3

Volume of a sphere = (6.28×3.375) / 3

Volume of a sphere = (21.195) / 3

Volume of a sphere = (21.195) / 3

Volume of a sphere = 7.065 cm3

volume of pencil = 7.065 cm3 + 42.39 cm3 + 7.065 cm3 = 56.52 cm3 

More lessons showing how to calculate the volume of solids.

Other common figures where the volume is calculated are shown below

Volume of a cube
Learn how to compute the volume of a cube.

Volume of a box
Learn how to compute the volume of a box or rectangular prism.

Volume of a sphere
Learn how to get the volume of a sphere. We have also included a calculator that will help you to practice and to check your answers.

Volume of an ellipsoid
Learn how to compute the volume of an ellipsoid. This lesson shows also how to get a radius when the volume and two radii are given.

Volume of cylinders
Learn how to compute the volume of cylinders and use an interactive calculator to practice and check your answers.

Volume of a cone
Learn how to get the volume of a cone and practice with an interactive calculator.

Volume of a pyramid
Learn how to get the volume of a pyramid.

Volume of irregular shapes
Learn how to get the volume of irregular shapes.

Volume or capacity
A solid introduction of volume and capacity and how to choose the best unit to measure capacity.


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