Answer:

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
![\sqrt[3]{\frac{1715}{1080}} = \frac{R}{r}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B1715%7D%7B1080%7D%7D%20%3D%20%5Cfrac%7BR%7D%7Br%7D)
Factorize
![\sqrt[3]{\frac{343*5}{216*5}} = \frac{R}{r}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B343%2A5%7D%7B216%2A5%7D%7D%20%3D%20%5Cfrac%7BR%7D%7Br%7D)
![\sqrt[3]{\frac{343}{216}} = \frac{R}{r}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B343%7D%7B216%7D%7D%20%3D%20%5Cfrac%7BR%7D%7Br%7D)

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 



<em>Hence, the curved surface area of the big cone is 1143.33cm^2</em>