1.2 Volume of Common Shapes

Note: volume is measured in units cubed (e.g. m^3, cm^3, mm^3, etc.).

Volume of a Sphere

  • The volume of a sphere is found using the formula:

V=\frac{4}{3} \pi r^{3}

Where r is the radius.

Picture 1

Example

Picture 2

We wish to find the volume of the above sphere. We do this by first identifying the values we need, in this case we have a radius of 10mm. Now, we substitute this value into our formula to find the volume

V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi 10^{3}=4188.79 \mathrm{~mm}^{3}

Volume of a Cylinder

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1.1 Surface Area of Common Shapes

Note: remember that area is measured in units squared (m^2, cm^2, etc.).

Surface Area of Spheres

  • The surface area of a sphere is found using:

A=4 \pi r^{2}

Where r is the radius of the sphere.

Example

Picture 2

We wish to find the surface area of the above sphere. We do this by first identifying the values we need, in this case we have a radius of 10mm. Now, we substitute this value into our formula to find the surface area:

A=4 \pi r^{2}=4 \pi 10^{2}=1256.64 \mathrm{~mm}^{2}

Surface Area of Cylinders

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