Question

The two cones are similar. The smaller cone has a surface area of 11.74 inches2.



Complete the last step to determine the surface area of the larger cone.

The scale factor of the larger to the smaller is , or .
The surface area will change by the square of the scale factor, which is , or .
Let the surface area of the larger cone be x. Then, the proportion is = .
Solve for x and round to the nearest hundredth. The surface area of the larger cone is about
inches2.

Answer 1

I don't have the scale factor (the problem statement left it blank). To finish the last step I need the linear scale factor (larger : smaller) or the corresponding lengths from the diagram.

General method / template:
- If the linear scale factor (larger to smaller) is k, then the surface area scale factor is k^2.
- So x = 11.74 · k^2.

Example: if the linear scale factor is 3/2 (1.5),
- k^2 = (3/2)^2 = 9/4 = 2.25
- x = 11.74 · 2.25 = 26.415 → rounded to nearest hundredth: 26.42 in^2.

Give me the missing scale factor (or the corresponding lengths) and I will compute the exact value and round it.