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