An ice-cream cone with a lid has a total surface area equal to the area of another circle of certain radius. If the radius of the circle is equal to average of the slant height and the radius of the cone, then the ratio of the slant height of the cone to the radius of the circle is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 3 : 2.
Radius of cone = r
Slant height of cone = l
Radius of circle = R = (l + r) / 2
⇒ πr(l + r) = πR2
⇒ r(l + r) = [(l + r) / 2]2
⇒ 4r = l + r
⇒ l = 3r
⇒ l / R = l / [(l + r) / 2] = 2l / (3r + r) = 2 × 3r / 4r = 3/2
The ratio is 3:2.