Question

A right cone has a surface area of 440 square inches and a radius of 7 inches. Find its slant height.

Answer 1

Answer:

Surface Area of right cone  

               =$\pi r(r+\sqrt{h^2 + r^2}$

$440 = \pi *7*(7+\sqrt{h^2+7^2})\\\\440 = 7\pi (7 + \sqrt{h^2+7^2})\\\\\frac{440}{7\pi } = 7 + \sqrt{h^2+49}\\\\\frac{440}{7\pi } - 7 = \sqrt{h^2+49}\\\\\frac{440-49\pi}{7\pi} =\sqrt{h^2+49}$

$\frac{286.062}{21.99} =\sqrt{h^2+49}\\\\13.0087= \sqrt{h^2+49}\\\\(13.0087)^2 = (\sqrt{h^2+49})^2\\\\169.227 = h^2 +49\\\\169.227 - 49 =h^2\\\\120.227 = h^2\\\\h = \sqrt{120.227} = 10.96in$