CPM Homework Help : APCALC Problem 4-25

A cone has a height of $10$ inches and a radius of $4$ inches. If a plane cuts the cone $h$ inches above the base of the cone, write an expression for the area of the circular cross-section.

Cone with vertex on top, dashed vertical segment labeled 10, from vertex to center of circular base, & dashed segment from center of base to edge of circle labeled 4, & circle around the cone, in top half, distance between circles labeled, h.

Hint:

Area of a circle $= πr^{2}$

Hint:

Sketch the radius and look for a geometric way to find its length.

Hint:

Do you see the similar triangles?

Hint:

Similar triangles have proportional sides, write a proportion to solve for $r$ . Be careful! The height of the small triangle is not $h$ .