The curved surface area of a cone is 7% of the curved surface area of a sphere. The slant height of the cone is equal to the radius of the sphere. The radius of the cone is 14 m. Find the difference between the height and the radius of the cone.

Correct answer: 34

Solution

Let the cone radius be 14 m and slant height be $l$. The curved surface area of the cone is $\pi rl = 14\pi l$, and that of the sphere is $4\pi R^2$, where $R=l$. Given $14\pi l = 7\% \times 4\pi l^2$, we get $14l = 0.28l^2$, so $l=50$ m. Then cone height $h = \sqrt{50^2-14^2} = 48$ m, so the difference between height and radius is $48-14=34$ m.

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