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?

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