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9.09 Surface area of composite solids

Lesson

So we know that surface area is the total area of all the faces on a 3D object.  We have looked at the surface area of prisms and cylinders, cones and pyramids and spheres.

Sometimes though the shape is a composite solid, (made up of a combination of other solids).  These are all composite solids.

To find the surface area of composite solids we need to be able to visualize the different shapes that make up the various surfaces. Once we have identified the different faces and shapes, calculate the areas of each face and add them up separately.

Don't forget to subtract faces which are not on the surface, like the circle where the cylinder sits on the rectangular prism in the middle image above.  

Other common mistakes to be careful about are to not forget faces you may not be able to see in the diagram like those at the back or on the bottom.  

Here are some worked examples.

Practice questions

Question 1

In the diagram, the roof has a height of $3$3 meters. Find the surface area of the figure shown,

Round your answer to two decimal places.

Question 2

Find the surface area of the figure shown,

correct to 2 decimal places.

QUESTION 3

We wish to find the surface area of the given solid.

  1. What is the surface area of the faces as seen from the top view?

  2. What is the surface area of the faces as seen from the left side view?

  3. What is the surface area of the faces as seen from the front view?

  4. Therefore, what is the total surface area, including all faces of the solid?

Outcomes

G.13

Use surface area and volume of three-dimensional objects to solve practical problems

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