Question

Two similar cones are shown in the image below.



What is the approximate surface area of the larger cone?

1,094.7 square yards

689.6 square yards

938.7 square yards

804.6 square yards

Answer 1

So, you're told that the cones are similar. Similar shapes have a common ratio between congruent parts. You have that the slant heights are 24 and 28. That gives you your ratio. Use that ratio to find out the larger cone's radius, and use that radius to find the surface area.

Answer 2

Give it a try and ask me any questions that come up.

Answer 3

corresponding parts*

Answer 4

1,094.7 square yards
===========
Find the surface area of the smaller cone.
It is 256 pi.

Because the cones are similar, the square of the scale factor is equal to the ratio of the areas.

(28/24)^2 = A /(256 pi)
A = 3136 pi /9 or 1094.6705 square yards

Answer 5

Here's how to figure out the radius:
Suppose A and a are corresponding parts of the two shapes and B and b are also corresponding parts. I can set up an equation like:
A/a = B/b

You know both of the slant heights, and you know the smaller radius. Use those things to set up that kind of equation.