Question

the lateral area of a cone with a diameter of 15 yards is about 287.5 square yards. to the nearest tenth, what is the slant height of the cone in yards?

Answer 1

Lateral area of the cone is given by:
LA=πr√(h²+r²)
where:
h=height
r=radius
Given that LA=287.5 yd² and r=(15/2) yds, then the height will be:
287.5=7.5π√(h²+7.5²)
solving for h we get:
(287.5/7.5π)²=h²+7.5²
thus
h²=(287.5/7.5π)²-7.5²
h²=63.1851597
 To get the slant height we use Pythagorean theorem.
c²=a²+b²
a²=h², b²=7.5²
thus
c²=h²+7.5²
c²=63.1851597+56.25
c²=119.4351597
c=10.92864~10.9 yards