CPM Homework Help : PCT Problem 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?

Step 1:

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

Equation

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

Step 2:

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

Cone pointing up, segment from vertex to center of circle base, labeled 10, with circle contained within the cone about 1 third down, segment from vertex to the upper circle labeled, x, radius on circle base meeting right edge of cone, labeled 4.