Verified answer

Assume:

Slant heights of the smaller and larger cones be 5p cm and 4p cm respectively and assume the diameter of both cones be d cm.

The curved surface area (CSA) of a cone is given by the formula:

CSA = πrl

(where r is the radius of the base of the cone and l is the slant height)

Since,

The diameters of both cones are equal their radii are also equal.

Assume the radius of the base of each cone be r cm.

Given :

The CSA of the smaller cone is 15.7 cm² and the ratio of the slant heights of the two cones is 5:4.

Therefore,

We can write the following equations:

πr5p = 15.7

πr4p = CSA of the larger cone

Dividing the second equation by the first equation :

[tex]\dfrac{\pi r4p}{\pi r5p}[/tex] = [tex]\dfrac{CSA\:of\:the\:larger\:cone}{15.7}[/tex]

[tex]\dfrac{4}{5}[/tex] = [tex]\dfrac{CSA\:of\:the\:larger\:cone}{15.7}[/tex]

We get:

CSA of the larger cone :

[tex]=\dfrac{4}{5}\times 15.7[/tex]

[tex]=\dfrac{62.8}{5}[/tex]

= 12.56 cm²

Therefore,

The CSA of the larger cone is 12.56 cm²