Lateral Surface Area

Question

A right circular cone is generated by revolving the region bounded by
y = 5x/12, y = 5, x = 0, about the y-axis. Find the lateral surface area of the cone.

Answer 1

Ahmad,

 

The lateral surface area is half the product of the cone's slant height and its circumference. The slant height is a right triangle with a height of 5, so if we set 5x/12=5, we get x=12. Now we know the radius of the cone is 12. We also know the slant height is the hypotenuse of a triangle with height 5 and base 12, giving us a slant height of 13. (Use Pythagorean theory here). Putting it altogether, .5*2*pi*12*13=489.84.

 

Hope that helps!