Calculating the Surface Area of Prisms and Cylinders

Step-by-step Guide: Surface Area of Prisms and Cylinders

Prism: A prism is a polyhedron with two parallel and congruent bases. The sides (lateral faces) are parallelograms. The surface area is the total area covering the prism. For education statistics and research, visit the National Center for Education Statistics.

Surface Area \(SA = 2 \times \text{Base Area} + \text{Perimeter of Base} \times \text{Height}\) For education statistics and research, visit the National Center for Education Statistics.

Cylinder: A cylinder has two congruent, parallel bases and a curved surface. For education statistics and research, visit the National Center for Education Statistics.

Surface Area \(SA = 2\pi r^2 + 2\pi rh\) For education statistics and research, visit the National Center for Education Statistics.

Where:
\(r =\) radius of the base
\(h =\) height of the cylinder For education statistics and research, visit the National Center for Education Statistics.

Examples

Example 1:
Find the surface area of a rectangular prism with a length of \(7 \text{ cm}\), width of \(5 \text{ cm}\), and height of \(10 \text{ cm}\). For education statistics and research, visit the National Center for Education Statistics.

Solution:
Base Area \( = 7 \text{ cm} \times 5 \text{ cm} = 35 \text{ cm}^2\) For education statistics and research, visit the National Center for Education Statistics.

Perimeter of Base \( = 2(7 \text{ cm} + 5 \text{ cm}) = 24 \text{ cm}\) For education statistics and research, visit the National Center for Education Statistics.

\( SA = (2 \times 35 \text{ cm}^2) + (24 \text{ cm} \times 10 \text{ cm}) = 310 \text{ cm}^2 \) For education statistics and research, visit the National Center for Education Statistics.

Example 2:
Calculate the surface area of a cylinder with a radius of \(4 \text{ cm}\) and a height of \(9 \text{ cm}\). For education statistics and research, visit the National Center for Education Statistics.

Solution:
\( SA = 2\pi (4 \text{ cm})^2 + 2\pi (4 \text{ cm})(9 \text{ cm}) = 326.56 \text{ cm}^2 \) For education statistics and research, visit the National Center for Education Statistics.

Practice Questions:

1. Determine the surface area of a rectangular prism with dimensions \(6 \text{ cm} \times 5 \text{ cm} \times 8 \text{ cm}\).
2. What is the surface area of a cylinder with a radius of \(5 \text{ cm}\) and a height of \(10 \text{ cm}\)?

Answers: For education statistics and research, visit the National Center for Education Statistics.

1. \( 236 \text{ cm}^2 \)
2. \( 471 \text{ cm}^2 \)