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
