Question

Given a cone with a radius of 8 ft and a height of 15ft. Find the area of the triangle formed by a perpendicular cross-section through the cone’s center.

Answer 1

you need to find the radius in the middle with similar triangles

Answer 2

I still don't understand >.<

Answer 3

okay, so we need to find the radius at the middle of the cone

\(\dfrac{8}{15}=\dfrac{x}{7.5}\)

\(x=\dfrac{8*7.5}{15}=4\)

now the problem of finding the maximum is a little complicated, it will be an equilateral triangle, look the link here for details.

http://math.ucsd.edu/~wgarner/math4c/randprob/areaprob/triangleincircle.htm

so the formula for the area is: \(A=\dfrac{\sqrt 3}{4}r^2\)

Answer 4

okay so just solve the formula right?

Answer 5

yep plug the radius (4~ ft) into the area formula. You should read over that link so you know how it was done.