The diameters of two cones are equal and their slant height are in the ratio 5 : 4. If the curved surface area of the smaller cone is 400 cm² then find the curved surface area of the bigger cone.

As the diameters of the cones are equal, their radius is also equal

Let the radius of both cones be r

Let the slant height of bigger cone be l₁ and that of smaller cone be l₂

l₁:l₂ = 5:4

⇒ =

Curved surface area of smaller cone = 400 cm²

Curved surface area of cone = πrl

Curved surface area of bigger cone = πrl₁

Curved surface area of smaller cone = πrl₂

Consider ratio of curved surface area of bigger cone to smaller cone

⇒ =

⇒ =

⇒ =

⇒ Curved surface area of bigger cone =

⇒ Curved surface area of bigger cone = 5 × 100

⇒ Curved surface area of bigger cone = 500 cm²

Therefore, curved surface area of bigger cone is 500 cm²