Finding the Angle of Cut for a Spherical Fruit Slice

[GeometryIsHARD]

Homework Statement

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.

Homework Equations

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

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?

 

[SteamKing]

Homework Statement

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.

Homework Equations

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

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?

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.

Hint: Google "sphere"

 

[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.
$\frac{\pi/8}{\theta} = \frac{Area}{2\pi}$