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.

Surface Area \(SA = 2 \times \text{Base Area} + \text{Perimeter of Base} \times \text{Height}\)

Cylinder: A cylinder has two congruent, parallel bases and a curved surface.

Surface Area \(SA = 2\pi r^2 + 2\pi rh\)

Where:
\(r =\) radius of the base
\(h =\) height of the cylinder

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 \(10 \text{ cm}\).

Solution:
Base Area \( = 7 \text{ cm} \times 5 \text{ cm} = 35 \text{ cm}^2\)

Perimeter of Base \( = 2(7 \text{ cm} + 5 \text{ cm}) = 24 \text{ cm}\)

\( SA = (2 \times 35 \text{ cm}^2) + (24 \text{ cm} \times 10 \text{ cm}) = 310 \text{ cm}^2 \)

Example 2:
Calculate the surface area of a cylinder with a radius of \(4 \text{ cm}\) and a height of \(9 \text{ cm}\).

Solution:
\( SA = 2\pi (4 \text{ cm})^2 + 2\pi (4 \text{ cm})(9 \text{ cm}) = 326.56 \text{ cm}^2 \)

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:

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