the volume of two similar solids are 1080cm and 1715cm .if the curved surface area of the smaller cone is 840cm .fond the curved surface area of the larger cone

Explanation:

The given parameters are:

Required

Determine the curved surface area of the big cone

The volume of a cone is:

For the big cone:

Where

R = radius of the big cone and H = height of the big cone

For the small cone:

Where

r = radius of the small cone and H = height of the small cone

Because both cones are similar, then:

and

Substitute values for Vbig and  Vsmall

Recall that:

So, we have:

Take cube roots of both sides

Factorize

The curved surface area is calculated as:

Where

For the big cone:

For the small cone

Because both cones are similar, then:

and

This gives:

Recall that:

So, we have:

Make the subject

Substitute values for and

Hence, the curved surface area of the big cone is 1143.33cm^2