Rudy414 wrote:An Architect is planning to incorporate several stone spheres of difference sizes into the lanscaping of a public park and workers who will be applying a finish to the exterior of the spheres need to know the surface area of each spere. The finishing process costs $92 per square meter. The surface area is equal to 4(pi)r^2, where r is the radius of the sphere.
Select the value that is the closest to the cost of finishing a sphere with a 5.50 meter circumference and the cost of finishing a sphere with a 7.85 meter circumference.
$900
$1,200
$1,800
$2,800
$3,200
$4,500
Thanks!
To apply the surface area formula, 4(pi)r^2, we need to calculate the radius of each sphere.
We know that circumference = 2(pi)(radius)
Sphere #1: 5.50 meter circumference
This means that 2(pi)(radius) = 5.5
So, radius =
5.5/(2pi)
Aside: in a moment, you'll see why I didn't evaluate
5.5/(2pi)
Now, we'll apply the surface area formula
Surface area = 4(pi)r^2
= 4(pi)
[5.5/(2pi)]^2
= 4(pi)
[30/(4pi^2)] ...
approximately
Aside: 5.5^2 = 30.25
There's a nice way to make this calculation in your head.
Here's a free video on how to do so:
https://www.gmatprepnow.com/module/gmat- ... ts?id=1024
Okay, moving along
Surface area = 4(pi)
[30/(4pi^2)]....
approximately
= 30/pi ....
approximately
= a number a little less than 10 (square meters)
Since each square meter of finishing costs $92, the total cost is a little less than $920
Only answer choice
A works
Sphere #2: 7.85 meter circumference
This means that 2(pi)(radius) = 7.85
So, radius =
7.85/(2pi)
Now, we'll apply the surface area formula
Surface area = 4(pi)r^
= 4(pi)
[7.85/(2pi)]^2
= 4(pi)
[60/(4pi^2)] ...
approximately
= 60/pi ....
approximately
= a number a little less than 20 (square meters)
Each square meter of finishing costs $92, so the total cost = (92)(20), which is approximately $1800
Only answer choice
C is close
Cheers,
Brent
