Dear Yumi,yumi2012 wrote:Thanks in advance
I'm happy to help.
Here's a text version of the question:
An architect is planning to incorporate several stone spheres of different sizes into the landscaping 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 sphere. The finishing process costs $92 per square meter. The surface area of a sphere is equal to 4(pi)r^2, where r is the radius of the sphere.
In the table, select the value of that closest to the cost of finishing a sphere with a 5.5-meter circumference as well as the cost of finishing a sphere with a 7.85-meter circumference.
First of all, notice circumference has the formula
c = 2(pi)r
Square this
c^2 = 4((pi)^2)(r^2)
But surface area (SA) = 4(pi)r^2
So
c^2 = 4((pi)^2)(r^2) = (pi)*[4(pi)r^2] = (pi)*SA
or
SA = (c^2)/(pi)
That's a hugely handy shortcut.
Now, we will briefly use the calculator to square the two circumferences ----
(5.5)^2 = 30.25
(7.85)^2 = 61.6225
Now, I am going to estimate like mad. For the first sphere,
Estimate (5.5)^2 as just 30, and estimate (pi) as 3. Then, SA = 10 sq meters
Estimate the cost as $90/ sq m, so total cost = 90*10 = $900, answer (A).
The second sphere has approximately double the (c^2), so it will be double the cost of the first ----- $1800, answer (C).
Does all this make sense?
Mike
