We know, the total surface area of cone=πrs+πr2, where s is the slant height and r is the radius of the base of the cone.
Given, s=2r.
Also, the total surface area =740 ft2.
∴πrs+πr2=740.
Substituting s=2r and π=3 in the above equation we get,
3×r×2r+3r2=740
⇒3×2r2+3r2=740
⇒6r2+3r2=740
⇒9r2=740
⇒r2=7409
⇒r2=82.22
⇒r=√82.22
⇒r=9.06.
We know, diameter d= twice of radius.
∴d=2r
⟹d=2×9.06
⟹d=18.12 ft.
Therefore, option A is correct.