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4-101.

A cone has a height of $10$ inches and a radius of $4$ inches. If a plane cuts the cone $x$ inches below the cone's peak, what is the area of the circular cross section?

Find $r$ first in terms of $x$ using proportions.

$\frac{10}{4}=\frac{x}{r}\text{ Solve for } r\text{ in terms of }x.$

Area $= π r^2$
Substitute your result for r into the area formula.