# Surface area

1. May 15, 2016

### GeometryIsHARD

1. The problem statement, all variables and given/known data
A spherical fruit has a radius of 1 inch. A slice has surface area of its peel equal to pi/8 . Determine the angle of cut for the slice.

2. Relevant equations
I'm sure there is a relevant equation here but I don't know it :-(

3. The attempt at a solution
So the radius is 1 inch, and the surface of the peel is equal to pi/8... I know that the volume of a sphere is 4/3*pi*r^3, maybe if i took the derivative i could get an equation for surface area? that would make sense because the units would be squared which is what surface area is... am i going the right direction here?

2. May 15, 2016

### SteamKing

Staff Emeritus
You can look up the formula for the surface area of a sphere. It's not something which is top secret.

I'm surprised you know the formula for the volume of a sphere, but not the formula for the SA.

3. May 17, 2016

### RUber

Yes. You can take the derivative of volume (with respect to radius) to get the surface area.
If you wanted to go nuts, you could even switch to spherical coordinates and take an integral.
$\rho = 1 \\ \phi \in [0, \pi] \\ \theta \in [0, 2\pi]$
$\int_{0}^{\pi}\int_0^{2\pi} \rho^2 \sin\phi d\theta d\phi$
Or, like Steamking said, start with the formula for surface area, and then this problem gets changed into a proportion.
$\frac{\pi/8}{\theta} = \frac{Area}{2\pi}$