• Support PF! Buy your school textbooks, materials and every day products Here!

Surface area

  • #1

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?
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666

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"
 
  • #3
RUber
Homework Helper
1,687
344
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}##
 

Related Threads on Surface area

Replies
34
Views
8K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
960
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
943
  • Last Post
Replies
2
Views
938
  • Last Post
Replies
2
Views
793
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
3
Views
572
  • Last Post
Replies
4
Views
7K
Top