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By placing strips of height $2\pi r$ along the radius axis, their tops form a linear graph. As the partition width goes to zero, the step-function approximation converges to the area under the line $y=2\pi x$.

Conditions: Function $f(r) = 2\pi r$ is linear; Partition width $\Delta r \to 0$

By placing strips of height $2\pi r$ along the radius axis, their tops form a linear graph. As the partition width goes to zero, the step-function approximation converges to the area under the line $y=2\pi x$.

Conditions: Function $f(r) = 2\pi r$ is linear; Partition width $\Delta r \to 0$