HELP PLEASE: Surface Area Problem: An artist who is not terribly creative, chooses to paint a large concrete hemisphere with a radius of 7 feet with the seven colors of the rainbow. There will be a cap of red at the top, then stripes of orange, yellow, green, blue, indigo, and finally violet in that order. The vertical height of each stripe is the same, one foot. (Note that this is not the curved length.) Some calculus students got into an argument about which color would require the most paint - the red at the top, the violet at the bottom, or perhaps one of the colors in between. (Finishing in comments below)......

Question

anonymous · Answer

Use your knowledge of calculus to impress the other students and settle their dispute. Determine which of the colors takes the most paint.

p0sitr0n · Answer

$$I=\int\limits dS = \int\limits \int\limits \left( \frac{ \delta r }{ \delta u} \times \frac{ \delta r }{ \delta v} \right) dudv$$
But since you have a sphere, you can use n = (x,y,z)/r, where r is the radius of your sphere (7 feet)

anonymous · Answer

I do have that formula, however I guess I don't know where to start with this. Do I find the surface area of the whole circle and start taking s.a of each inner circle and subtract them?

anonymous · Answer

Is anyone available to clarify this for me?  I don't know what to do to get started.  I have the formula but don't know what to do with it to find each stripe.