1. Surface Area of Composite Solids
Lesson 16
Surface Area & Volume
Surface Area of Composite Solids

2. Warm-Up
Give the formula for calculating the surface area of a prism, cylinder, cone or pyramid.
Find the area of each composite figure. Use 3.14 for .
Round to the nearest hundredth, as needed. 3.

3. Surface Area of Composite Solides
Target: Calculate the surface area of composite solids.

4. Vocabulary Composite Solid: A three-dimensional figure made of
more than one solid.

5. Surface Area of Composite Solids
Identify the different types of figures that make the solid.
Identify which parts of each figure are on the surface of the solid.
Calculate the area of all parts on the surface.
Find the sum of the areas.

6. Example 1 Find the surface area of the composite solid.
This solid is made up of a square prism and a square pyramid.
Identify the parts of the solid on the surface.
1 Base LA of prism LA of Pyramid
Find the area of the base. (10)(10) = 100
Find the lateral area of prism. LA = Ph = 40(32) = 1280
Find the lateral area of pyramid. LA = Pl = (40)(12) = 240
Find the sum of all the three parts.
SA = = 1620
The surface area of the composite solid is 1,620 square feet.

7. Example 2
Find the surface area of the composite solid. Use 3.14 for π.
This composite solid is made of a cylinder and two cones.
Identify the parts of the solid on the surface.
LA of cylinder LA of cone on right LA of cone on left
Find LA of the cylinder LA = 2πrh ≈ 2(3.14)(2)(3) ≈ 37.68
Find LA of the right cone. LA = πrl ≈ (3.14)(2)(4) ≈ 25.12
Find LA of the left cone. LA = πrl ≈ (3.14)(2)(3) ≈ 18.84
Find the sum of all three parts.
SA = ≈ 81.64
The surface area of the composite solid is 81.64 m2.

8. Exit Problem
Find the surface area of the composite figure.

9. Communication Prompt
Which composite solid do you prefer finding the surface area of? Why?
Draw your own composite solid and describe how to find the surface area of it.