Answer:
Part 1) The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900
Part 2) The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800
Step-by-step explanation:
Step 1
Find the radius of each sphere
we know that
The circumference of a circle is equal to

<u><em>Find the radius of the sphere with a 5.50-meter circumference</em></u>
For 
assume

substitute and solve for r

![r=5.50/[2(3.14)]=0.88\ m](https://tex.z-dn.net/?f=r%3D5.50%2F%5B2%283.14%29%5D%3D0.88%5C%20m)
<u><em>Find the radius of the sphere with a 7.85-meter circumference</em></u>
For 
assume

substitute and solve for r

![r=7.85/[2(3.14)]=1.25\ m](https://tex.z-dn.net/?f=r%3D7.85%2F%5B2%283.14%29%5D%3D1.25%5C%20m)
step 2
Find the surface area of each sphere
The surface area of sphere is equal to

<u><em>Find the surface area of sphere with a 5.50-meter circumference</em></u>
For 
assume

substitute


<u><em>Find the surface area of sphere with a 7.85-meter circumference</em></u>
For 
assume

substitute


step 3
Find the cost of finishing each sphere
we know that
To find out the cost , multiply the surface area by $92 per square meter
<u><em>Find the cost of sphere with a 5.50-meter circumference</em></u>

therefore
The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900
<u><em>Find the cost of sphere with a 7.85-meter circumference</em></u>

therefore
The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800