Question

What is the area of the Red Cross-section??? PLEASE HELP!!!!

Answer 1

X is the radius of the slice.  So we must find the equation of the side of the cone.

y=mx+b, so now we must use two points to solve for the slope, or "m".

m=(y2-y1)/(x2-x1)

m=(0-15)/(5-0)

m=-15/5

m=-3  so our line so far is:

y=-3x+b, b=y-intercept=value of y when x=0, which we can see is 15 ft so:

y=-3x+15

Now the radius is x, so we must solve for x from the equation above...

-3x+15=y  subtract 15 from both sides

-3x=y-15  divide both sides by -3

x=(15-y)/3

And area of this circle is:

A=πx^2, and using x found above:

A=(π/9)(15-y)^2

A=(π/9)(225-30y+y^2), so when y=6 ft

A=(π/9)(225-30*6+6^2)

A=(π/9)(81)

A=9π or if we let π=pi

A=9pi ft^2