Determining the surface area on a 5 sided lunar esque shape

In summary, the surface area of a banana peel can be found by multiplying the length and width of each side by 5.
  • #1
GeometryIsHARD
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Homework Statement


I'm trying to figure out the surface area on a 5 sided shape where the sides can all be modeled by "lunes". The shape will end up looking like a banana peel. We are modeling the sides of the shape as lunes with varying angles on a sphere of radius 3 inches. I'm trying to figure out how I would determine the surface area of the banana peel.

Homework Equations

The Attempt at a Solution


Let me begin by saying I am quite confused... I have done a lot of thinking on this problem but seemingly to no avail. If I have 5 sides, could I do a length x width for each side and multiply it by 5? I need one of you genius's on this forum to help me understand what's going on here!
 
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  • #2
GeometryIsHARD said:

Homework Statement


I'm trying to figure out the surface area on a 5 sided shape where the sides can all be modeled by "lunes". The shape will end up looking like a banana peel. We are modeling the sides of the shape as lunes with varying angles on a sphere of radius 3 inches. I'm trying to figure out how I would determine the surface area of the banana peel.

Homework Equations

The Attempt at a Solution


Let me begin by saying I am quite confused... I have done a lot of thinking on this problem but seemingly to no avail. If I have 5 sides, could I do a length x width for each side and multiply it by 5? I need one of you genius's on this forum to help me understand what's going on here!
What makes you think that the area of one lune = length multiplied by the width? How closely do your lunes resemble rectangles?
 
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  • #3
Ah, i suppose not very close, was just taking a shot in the dark. Is there a similar equation for this situation? It must be a bit more complicated because it would include angles and radius of the sphere I suppose.
 
  • #4
GeometryIsHARD said:
Ah, i suppose not very close, was just taking a shot in the dark. Is there a similar equation for this situation? It must be a bit more complicated because it would include angles and radius of the sphere I suppose.
It's not clear what this shape looks like, but here is more information on the geometry of spherical lunes:

https://en.wikipedia.org/wiki/Spherical_lune
 
  • #5
so the surface area of a spherical lune is given by 2*θ*R^2, and since there are five lunes would it just be this multiplied by 5?
 
  • #6
GeometryIsHARD said:
so the surface area of a spherical lune is given by 2*θ*R^2, and since there are five lunes would it just be this multiplied by 5?
As long as each lune is identical in having the same angle θ.

You've never attached a picture of this figure, so I can't say for certain. :frown:
 
  • #7
a banana peel where each side can be modeled as a lune
 

1. How do you measure the surface area of a 5 sided lunar esque shape?

To measure the surface area of a 5 sided lunar esque shape, you can use the formula A = (5/2)s * l, where A is the surface area, s is the length of one side, and l is the apothem (distance from the center of the shape to the midpoint of one side). This formula is specifically for a pentagon, which is a 5 sided shape.

2. Can you use the same formula to measure the surface area of any 5 sided shape?

No, the formula A = (5/2)s * l is specifically for a pentagon. Other 5 sided shapes, such as a star or a cross, will have different formulas for calculating their surface area. It is important to identify the specific shape and use the appropriate formula.

3. How does the number of sides affect the surface area of a shape?

The number of sides of a shape does affect its surface area. Generally, the more sides a shape has, the larger its surface area will be. This is because a shape with more sides has more surface area to cover, compared to a shape with fewer sides.

4. Can you determine the surface area of a 5 sided lunar esque shape without measuring the sides?

Yes, it is possible to determine the surface area of a 5 sided lunar esque shape without measuring the sides. This can be done by using the Pythagorean theorem to find the length of the sides, and then plugging that value into the formula A = (5/2)s * l.

5. Is there a more accurate way to measure the surface area of a 5 sided lunar esque shape?

There are various methods for measuring the surface area of a shape, including using digital software or 3D scanning. These methods may provide more accurate measurements compared to manually measuring the sides and using a formula. However, the accuracy also depends on the precision of the measuring tools and the complexity of the shape.

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