Question

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

Answer 1

Surface Area of right cone

=
`\pi r(r+√(h^2 + r^2)`

`440 = \pi *7*(7+√(h^2+7^2))\\\\440 = 7\pi (7 + √(h^2+7^2))\\\\(440)/(7\pi ) = 7 + √(h^2+49)\\\\(440)/(7\pi ) - 7 = √(h^2+49)\\\\(440-49\pi)/(7\pi) =√(h^2+49)\\\\`

`(286.062)/(21.99) =√(h^2+49)\\\\13.0087= √(h^2+49)\\\\(13.0087)^2 = (√(h^2+49))^2\\\\169.227 = h^2 +49\\\\169.227 - 49 =h^2\\\\120.227 = h^2\\\\h = √(120.227) = 10.96in`