Unit 6-Lesson 8 Surface area of composite 3-D figures practice
1. Find the surface area of the composite figure shown below.
- The figure consists of a rectangular prism with dimensions 4 cm x 6 cm x 8 cm and a cylinder with radius 3 cm and height 10 cm.
To find the surface area of the composite figure, we need to find the surface area of both the rectangular prism and the cylinder separately and then add them together.
Surface area of the rectangular prism:
- 2(4*6) + 2(4*8) + 2(6*8) = 48 + 64 + 96 = 208 cm²
Surface area of the cylinder:
- 2πr² + 2πrh = 2(3.14*3²) + 2(3.14*3*10) = 56.52 + 188.4 = 244.92 cm²
Total surface area of the composite figure:
- 208 + 244.92 = 452.92 cm²
Therefore, the surface area of the composite figure is 452.92 cm².
2. Find the surface area of the composite figure shown below.
- The figure consists of a cube with edge length 5 cm and a hemisphere with radius 4 cm.
To find the surface area of the composite figure, we need to find the surface area of both the cube and the hemisphere separately and then add them together.
Surface area of the cube:
- 6a² = 6(5*5) = 150 cm²
Surface area of the hemisphere:
- 2πr² + πr² = 2(3.14*4²) + 3.14*4² = 100.48 cm²
Total surface area of the composite figure:
- 150 + 100.48 = 250.48 cm²
Therefore, the surface area of the composite figure is 250.48 cm².