surface area of composite 3d figures practice
1. Find the surface area of a rectangular prism with dimensions 4 cm by 5 cm by 6 cm.
First, calculate the surface area of each face:
- Front and back faces: 4 cm x 6 cm = 24 cm² x 2 = 48 cm²
- Top and bottom faces: 4 cm x 5 cm = 20 cm² x 2 = 40 cm²
- Side faces: 5 cm x 6 cm = 30 cm² x 2 = 60 cm²
Then add up all the areas:
48 cm² + 40 cm² + 60 cm² = 148 cm²
Therefore, the surface area of the rectangular prism is 148 cm².
2. Find the surface area of a cylinder with a radius of 3 cm and height of 8 cm.
First, calculate the lateral surface area of the cylinder:
- Lateral surface area = 2πrh
- Lateral surface area = 2 x 3.14 x 3 cm x 8 cm
- Lateral surface area = 150.72 cm²
Then, calculate the surface area of the two circular bases:
- Area of a circle = πr²
- Area of each base = 3.14 x (3 cm)²
- Area of each base = 28.26 cm² x 2 = 56.52 cm²
Finally, add up the lateral surface area and the area of the two bases:
150.72 cm² + 56.52 cm² = 207.24 cm²
Therefore, the surface area of the cylinder is 207.24 cm².
3. Find the total surface area of a cone with a radius of 4 cm and slant height of 7 cm.
First, calculate the lateral surface area of the cone:
- Lateral surface area = πrl
- Lateral surface area = 3.14 x 4 cm x 7 cm
- Lateral surface area = 87.92 cm²
Then, calculate the base area of the cone:
- Base area = πr²
- Base area = 3.14 x (4 cm)²
- Base area = 50.24 cm²
Finally, add up the lateral surface area and the base area:
87.92 cm² + 50.24 cm² = 138.16 cm²
Therefore, the total surface area of the cone is 138.16 cm².