Finding Surface Area of Sphere with Illuminated Light Question

In summary, the conversation discusses finding the surface area of a sphere illuminated by a light held at a distance h from its surface. The person seeking help is unsure of how to approach the problem and has already drawn a diagram. The conversation then offers suggestions for finding the solution, including drawing tangent lines and considering a cross-section as a surface of revolution. References to arc length and surface integrals are also mentioned, with a link provided for further clarification.
  • #1
zachem62
37
3

Homework Statement

Find the surface area of a sphere of radius R that is illuminated by a light that is held h units away from its surface.

Homework Equations



integral surface area formula i don't know how to type it up properly on here.

The Attempt at a Solution


I have NO idea how to do this problem. Please help! Thanks!
 
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  • #2
zachem62 said:

Homework Statement




Find the surface area of a sphere of radius R that is illuminated by a light that is held h units away from its surface.


Homework Equations



integral surface area formula i don't know how to type it up properly on here.

The Attempt at a Solution


I have NO idea how to do this problem. Please help! Thanks!

Start by drawing a diagram of the setup...
 
  • #3
berkeman said:
Start by drawing a diagram of the setup...
I've already drawn a diagram I just couldn't put it up here that's all.
 
  • #4
zachem62 said:
I've already drawn a diagram I just couldn't put it up here that's all.

There are several ways to post your diagram and show your work. What format is it in? If hand-drawn, can you scan it or snap a picture of it on your phone? If it is in Visio or other drawing program, convert it to PDF (like using PrimoPDF) and attach it to your reply.
 
  • #5
Draw lines from the light tangent to the sphere. That gives you the illuminated area.
 
  • #6
Also think about a cross-section and treating it as a surface of revolution.
 
  • #7
I'm not entirely sure where you encounter difficulty?

A lot of people get stuck for a time on arc length and surface integrals (I did). If that's it, maybe this link will help:

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-b-partial-fractions-integration-by-parts-arc-length-and-surface-area/session-79-surface-area/MIT18_01SCF10_Ses79b.pdf

If that's clear, then you just need to figure out where to put the lower limit on the definite integral. Try drawing a diagram and look for similar triangles. I'm including two attachments, pdf files I made myself.

I wonder if I could just attach that MIT file ... it's being distributed freely anyway.
 

Attachments

  • Light on Sphere.pdf
    39.4 KB · Views: 242
  • Light on Sphere GSP.pdf
    95.6 KB · Views: 235
  • MIT18_01SCF10_Ses79b.pdf
    165.9 KB · Views: 464
Last edited by a moderator:

Related to Finding Surface Area of Sphere with Illuminated Light Question

1. What is surface area and why is it important?

Surface area is the measurement of the total area that the surface of an object covers. It is important in science because it helps us understand how much of an object's surface is exposed and can affect its properties, such as its ability to absorb or release heat or interact with other substances.

2. How is surface area calculated?

The formula for calculating surface area varies depending on the shape of the object. For example, the surface area of a cube is calculated by multiplying the length of one side by itself, then multiplying that result by 6 (since a cube has 6 equal sides). It is important to know the specific formula for the shape you are dealing with in order to accurately calculate the surface area.

3. What are some real-life applications of surface area?

Surface area is used in many fields, such as chemistry, physics, and engineering. Some examples of its applications include calculating dosage amounts of medication, determining the efficiency of heat exchangers, and designing more aerodynamic structures.

4. How does surface area affect the rate of reactions?

The larger the surface area of a substance, the more exposed it is to other substances, making it easier for reactions to occur. This is because there is a larger area for molecules to interact with each other. For example, grinding a solid into a powder increases its surface area and can make it react faster with other substances.

5. Can surface area be changed?

Yes, surface area can be changed by altering the shape, size, or texture of an object. For example, breaking a solid into smaller pieces or stretching a material to create a larger surface area can change its properties and how it interacts with other substances.

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