# How the Area of a Disk Grows

How the Area of a Disk Grows

An increase in the radius of a circular disk leads to a corresponding increase in the area of the disk. Geometrically, is the red annulus. Slicing and then unrolling this annulus would yield a shape close to a rectangle with base and height . This gives the approximation . Using the slider, notice this approximation is quite accurate for close to zero. Graphing the area as a function of the radius , the ratio is the slope of a secant line to the curve. Dividing both sides of by implies the slope may be approximated by the circumference .

ΔR

ΔA

ΔA

2πR

ΔR

ΔA≈2πRΔR

ΔR

A

R

ΔA/ΔR

ΔA≈2πRΔR

ΔR

ΔA/ΔR

2πR