1.3 Surface Area and Volume of Composite Shapes

Note: if you cannot remember the formulas for the surface area and volume of common shapes, revise notes for 1.1 Surface Area of Common Shapes and 1.2 Volume of Common Shapes.

Guide to Finding the Surface Area of a Composite Shape

  • Composite shapes are shapes that are created by merging multiple simple shapes.
  • Due to the large amount of combinations possible, it is not possible to derive formulas for each.
  • To find the surface area of a composite shape, you need to first identify the simple shapes it is made up of. The surface area of the composite shape is equal to the sum of each shape, minus the surface area which has been removed to merge it into the shape:
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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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