Problem

A cylinder has radius \(r\) and height \(h\). Identify the student setup that gives its total surface area.

Student 1: \(2\pi~\text{rh}\)
Student 2: \(\pi~r^{2}h\)
Student 3: \(2\pi~r^{2}~+~2\pi~\text{rh}\)
Student 4: \(\pi~r^{2}~+~2\pi~\text{rh}\)

Big Picture

What this problem is really about

Judge each setup against the complete exterior of a closed cylinder. It must contain two circle-area terms for the bases and a separate circumference-times-height term for the curved side. A missing base gives only part of the surface, while multiplying base area by height changes the quantity to volume.

Answer choices

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Preview only

Student 2: πr²h

Student 1: 2πrh

Student 3: 2πr² + 2πrh

Student 4: πr² + 2πrh

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A cylinder has radius \(r\) and height \(h\). Identify the student setup that gives its total surface area.

Student 1: \(2\pi~\text{rh}\)
Student 2: \(\pi~r^{2}h\)
Student 3: \(2\pi~r^{2}~+~2\pi~\text{rh}\)
Student 4: \(\pi~r^{2}~+~2\pi~\text{rh}\)

What this problem is really about

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A cylinder has radius \(r\) and height \(h\). Identify the student setup that gives its total surface area.Student 1: \(2\pi~\text{rh}\)Student 2: \(\pi~r^{2}h\)Student 3: \(2\pi~r^{2}~+~2\pi~\text{rh}\)Student 4: \(\pi~r^{2}~+~2\pi~\text{rh}\)

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.

A cylinder has radius \(r\) and height \(h\). Identify the student setup that gives its total surface area.

Student 1: \(2\pi~\text{rh}\)
Student 2: \(\pi~r^{2}h\)
Student 3: \(2\pi~r^{2}~+~2\pi~\text{rh}\)
Student 4: \(\pi~r^{2}~+~2\pi~\text{rh}\)