Surface Area Of Cylinders In Terms Of Pi

✏️ Worked Example

Cylinder with Radius 5 cm and Height 9 cm

Given:

Radius: \(r = 5\text{ cm}\)

Height: \(h = 9\text{ cm}\)

Step 1: Use the formula.

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

Step 2: Substitute the values.

\(SA = 2\pi(5)^2 + 2\pi(5)(9)\)

Step 3: Simplify each part.

\(2\pi(25) = 50\pi\)

\(2\pi(5)(9) = 90\pi\)

Step 4: Add the terms.

\(SA = 50\pi + 90\pi\)

\(SA = 140\pi\)

Surface Area:

\(SA = 140\pi\text{ cm}^2\)

🧠 Math Vocabulary

• cylinder: a three-dimensional figure with two congruent circular bases and one curved surface.
• radius: the distance from the center of a circle to the edge of the circle.
• height: the distance between the two circular bases of the cylinder.
• base area: the area of one circular base, found using \(A=\pi r^2\).
• lateral area: the area around the side of the cylinder, found using \(2\pi rh\).
• in terms of \(\pi\): an exact answer that leaves \(\pi\) in the final expression instead of using a decimal approximation.
• square units: units used to measure area, such as \(\text{cm}^2\), \(\text{in}^2\), or \(\text{ft}^2\).

📚 What You Should Already Know

Students should know how to square a number, multiply terms with \(\pi\), find the area of a circle using \(A=\pi r^2\), and understand that surface area measures the total outside covering of a three-dimensional figure.

🚀 What Comes Next

After finding cylinder surface area in terms of \(\pi\), students can practice using decimal approximations of \(\pi\), compare exact and approximate answers, and apply cylinder surface area to real-world problems involving cans, labels, containers, and packaging.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube Short directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.