L3 · Surface Area of Right Cylinders

Learning goal

“I can find the surface area of a right cylinder from its net - two circles plus one rectangle whose length is the circumference - SA = 2πr² + 2πrh, and I can adjust the formula for an open cylinder (one end, or no ends).”

Right cylinder — a prism-family solid with two congruent circular bases and a curved side that unrolls into a rectangle.

Lateral surface area — the area of the curved side alone: 2πrh. Think label, wrapper, or paint on the side.

Net of a cylinder — two circles and one rectangle. The rectangle's length is exactly the circumference of the circles (2πr); its width is the cylinder's height.

Open cylinder — a cylinder missing one end (an open-top tank) or both ends (a pipe, a tube). The formula changes: count only the ends that exist.

Worked example

A closed right cylinder has radius 3 cm and height 8 cm. Find its surface area. Step 1: Sketch the net: two circles, one rectangle. Step 2: Ends: 2 x π x 3² = 2 x 9π = 18π cm2. Step 3: Side: the rectangle's length is the circumference, 2π x 3 = 6π; area = 6π x 8 = 48π cm2. (Formula form: 2πrh = 2π x 3 x 8 = 48π.) Step 4: SA = 18π + 48π = 66π ≈ 207.35 cm2. Estimate check: roughly a 6 by 8 by ... the ends are small (about 28 each), the side is about 151 - 207 is in range.

Check yourself — explain it

In the formula term 2πrh, where does the 2πr come from?

Paired problem — example still visible

Closed cylinder, r = 4 cm, h = 6 cm -> ends 2 x 16π = 32π; side 2π x 4 x 6 = 48π; SA = 80π ≈ 251.33 cm2

Faded completion — last step is yours

"Closed cylinder, r = 2 cm, h = 10 cm: SA = 2π(4) + 2π(2)(10) = 8π + ___π = ___π ≈ ___ cm2" -> 40π; 48π ≈ 150.80 cm2

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz

Grade 10 — Mathematics 10C › C10U02 Surface Area & Volume

L3 · Surface Area of Right Cylinders