November 10, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Volume - Prisms, Cylinders, Cones, Pyramids and Spheres.

In this mini-lesson you'll learn how to calculate the Volume of common solids. It will be presented with the help of some examples, practice questions with solution and using video explanation in own handwriting by the instructor.

Let us explore how to find volumes of prisms:

Volume of a prism = Area of base x height =*l w h*

where*l* is length, *w* is width and *h* is height of the prism. E.g. to find the volume of a rectangular prism with dimensions are 12 cm, 6 cm and 8 cm., substitute values of dimensions in the above formula i.e. 12 x 6 x 8, which gives 576 cm^{3}.

Volume of a pyramid = 1/3 x Area of base x height = 1/3 x B x*h*

where B is area of the base and*h* is the height of pyramid. For example, if the base of a pyramid has an area 50 m^{2} and its height is 10 m, then the volume of the pyramid is 166.7 m^{3}.

Volume of cylinder = Base x height = B x*h* = ?*r*^{2} x *h* = ?*r*^{2}*h*

where B is the base and*h* is the height. E.g. to find the volume of cylinder having diameter of 6 in and a height of 12 in, first let us calculate the radius of the base i.e. *r* = 6/2 = 3 in. Now plug in values of *r* and *h* in the formula for volume of cylinder i.e. ?(3)^{2} x 12. It works out to 108? in^{3}.

Volume of cone = 1/3 x Base x height = 1/3 x B x*h*

where B is the base area and*h* be the height of the cone. E.g. if a circle with a diameter of 6 units from the base of a cone having a height of 21 units, then the volume of a cone is given by 1/3 x ? x (3)^{2} x 21, which results in 197.9 cubic units.

Volume of sphere = 4/3 ?*r*^{3}

where*r* is the radius of sphere. E.g. to find the volume of the sphere with radius 14 cm, plug in 14 for *r* in above formula i.e. 4/3 x ?(14)^{3}, and this works out to 11494 cm^{3}.

In this mini-lesson you'll learn how to calculate the Volume of common solids. It will be presented with the help of some examples, practice questions with solution and using video explanation in own handwriting by the instructor.

Let us explore how to find volumes of prisms:

Volume of a prism = Area of base x height =

where

Volume of a pyramid = 1/3 x Area of base x height = 1/3 x B x

where B is area of the base and

Volume of cylinder = Base x height = B x

where B is the base and

Volume of cone = 1/3 x Base x height = 1/3 x B x

where B is the base area and

Volume of sphere = 4/3 ?

where

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

- Mathematics > General
- Mathematics > Geometry
- Education > General

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Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.