I don't understand this problem -- Surface area of a section of a solid sphere

In summary, the problem is asking for the area of the partial sphere surface, plus the three other sides.
  • #1
samy4408
62
9
Homework Statement
...
Relevant Equations
...
Sorry i don't understand English very well , if someone want to explain to me this problem?
2022-03-04 18_34_35-Window.png
 
Physics news on Phys.org
  • #2
What part is giving you difficulty?
Try your best to explain what you think it's asking for. We'll see of we can set you straight.
 
  • #3
samy4408 said:
Homework Statement:: ...
Relevant Equations:: ...

Sorry i don't understand English very well , if someone want to explain to me this problem?
View attachment 297876
Ordinarily I would delete a post like this, as there is no work shown, but today is your lucky day.
Do you know a formula for the surface area of a sphere whose radius is given?
Can you determine what fraction of a sphere is shown in the picture?
 
  • #4
The problem is asking you to calculate the surface of a sphere that has been cut as shown.
Can you see it tridimensional in your head?
 
  • #5
Mark44 said:
Ordinarily I would delete a post like this, as there is no work shown, but today is your lucky day.
Do you know a formula for the surface area of a sphere whose radius is given?
Can you determine what fraction of a sphere is shown in the picture?
I do know the formula for the surface area of a sphere , the problem is what they are asking for ,
is it the surface of the sphere that is shown ? is it 1/8 of the total surface of the sphere ?
 
  • #6
samy4408 said:
is it 1/8 of the total surface of the sphere ?
yes
 
  • #7
phinds said:
yes
No. You also have to add on the new faces from the cut.
 
  • Like
Likes DaveC426913 and PeroK
  • #8
phinds said:
yes
So it is 2*pi
 
  • #9
caz said:
No. You have to add on the new faces from the cut.
Ah. You are right of course. I missed that they want ALL of the surface area. Still a trivial problem.
 
  • #10
samy4408 said:
So it is 2*pi
That's just the surface area of the part of the sphere. The problem is asking for the area of the partial sphere surface, plus the three other sides.
 
  • #11
caz said:
No. You also have to add on the new faces from the cut.
It says a "solid sphere", so this is correct, IMO. If it was just a spherical surface that was cut, it would be different.
 
  • #12
Well boo. You guys moved on while I was busy rendering a visual aid.

1646420491341.png
 
  • Like
Likes jim mcnamara, Frabjous and PeroK

1. How do I calculate the surface area of a section of a solid sphere?

The surface area of a section of a solid sphere can be calculated by first finding the area of the full sphere using the formula A = 4πr², where r is the radius of the sphere. Then, multiply this value by the fraction of the sphere that is represented by the section. For example, if the section is a semicircle, the fraction would be 1/2.

2. What is the difference between surface area and volume?

Surface area refers to the total area of all the faces or surfaces of a 3-dimensional object. Volume, on the other hand, refers to the amount of space that an object occupies. In the case of a solid sphere, surface area would refer to the total area of the curved surface, while volume would refer to the amount of space inside the sphere.

3. Can the surface area of a section of a solid sphere be greater than the surface area of the full sphere?

No, the surface area of a section of a solid sphere will always be less than or equal to the surface area of the full sphere. This is because the section is always a fraction of the full sphere, and the surface area of a sphere increases as the radius increases.

4. How does the size of the section affect the surface area of a solid sphere?

The size of the section directly affects the surface area of the solid sphere. The larger the section, the greater the surface area will be. This is because a larger section represents a larger fraction of the full sphere, resulting in a larger surface area calculation.

5. Are there any real-world applications of calculating the surface area of a section of a solid sphere?

Yes, there are many real-world applications of calculating the surface area of a section of a solid sphere. For example, this calculation is used in engineering and construction to determine the amount of material needed to create curved structures, such as domes or arches. It is also used in physics and astronomy to calculate the surface area of planets and other celestial bodies.

Similar threads

Surface area of a sphere ##= \pi * (a^2+b^2+c^2+d^2)##
    • Precalculus Mathematics Homework Help
Replies
18
Views
1K
I Surface charge of neutral solids
    • Electromagnetism
Replies
3
Views
1K
I Calculating the surface area of a sphere using dA
    • Calculus
Replies
33
Views
3K
I Surface area and length (percent increase relationship)
    • Classical Physics
Replies
6
Views
1K
Find the Area of the Shaded Section in a Circle
    • Precalculus Mathematics Homework Help
Replies
12
Views
1K
I Help with FLP argument of non-uniformly distributed surface charges
    • Electromagnetism
Replies
2
Views
683
Rates of change: surface area and volume of a sphere
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Why is the pressure on a charged sphere only exerted on the contact area?
    • Introductory Physics Homework Help
Replies
6
Views
1K
Capacitance of an isolated sphere - solid vs hollow
    • Electromagnetism
Replies
1
Views
9K
Why are the three different surface tensions in the directions shown?
    • Introductory Physics Homework Help
Replies
4
Views
638

Hot Threads

Recent Insights

Back
Top