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

Linear approximation of paint

  • Thread starter Weave
  • Start date
  • #1
143
0

Homework Statement


Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.100000 cm thick to a hemispherical dome with a diameter of 45.000 meters.

Homework Equations


[tex]Surface Area of sphere=4\pi(r^2)[/tex]
Since it is hemipshereical, the surface area will be half
[tex]Surface Area of hemispherical dome=2\pi(r^2)[/tex]
[tex]dSA=4\pi(r)dr[/tex]


The Attempt at a Solution


I converted 45m into 4500cm for the radius. I set dr=.1cm
and the radius to 4500cm.
 
Last edited:

Answers and Replies

  • #2
nrqed
Science Advisor
Homework Helper
Gold Member
3,599
203

Homework Statement


Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.100000 cm thick to a hemispherical dome with a diameter of 45.000 meters.

Homework Equations


[tex]Surface Area of sphere=4\pi(r^2)[/tex]
Since it is hemipshereical, the surface area will be half
[tex]Surface Area of hemispherical dome=2\pi(r^2)[/tex]
[tex]dSA=4\pi(r)dr[/tex]


The Attempt at a Solution


I converted 45m into 4500cm for the radius. I set dr=.1cm
and the radius to 4500cm.
The question says that 45 m is the diameter, not the radius.
 
  • #3
143
0
Oops. Well I inputed 2250cm for the radius and it is still wrong
 
Last edited:
  • #4
143
0
Am I approaching this the right way?
 
  • #5
Dick
Science Advisor
Homework Helper
26,258
618
This time the problem is to determine a volume. So you want to estimate the change in volume if a hemisphere grows from diameter 45m to 45.002m.
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
41,805
932

Homework Statement


Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.100000 cm thick to a hemispherical dome with a diameter of 45.000 meters.

Homework Equations


[tex]Surface Area of sphere=4\pi(r^2)[/tex]
Since it is hemipshereical, the surface area will be half
[tex]Surface Area of hemispherical dome=2\pi(r^2)[/tex]
[tex]dSA=4\pi(r)dr[/tex]


The Attempt at a Solution


I converted 45m into 4500cm for the radius. I set dr=.1cm
and the radius to 4500cm.
As you have been told the DIAMETER is 45 m. so the radius is 22.5 m= 2250 cm. In addition, YOU said
Since it is hemipshereical, the surface area willbe half
[tex]Surface Area of hemispherical dome=2\pi(r^2)[/tex]
but then say
[tex]dSA=4\pi(r)dr[/tex]
Shouldn't it be
[tex]dSA= 2\pi r^2 dr[/tex]?
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,805
932

Homework Statement


Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.100000 cm thick to a hemispherical dome with a diameter of 45.000 meters.

Homework Equations


[tex]Surface Area of sphere=4\pi(r^2)[/tex]
Since it is hemipshereical, the surface area will be half
[tex]Surface Area of hemispherical dome=2\pi(r^2)[/tex]
[tex]dSA=4\pi(r)dr[/tex]


The Attempt at a Solution


I converted 45m into 4500cm for the radius. I set dr=.1cm
and the radius to 4500cm.
As you have been told the DIAMETER is 45 m. so the radius is 22.5 m= 2250 cm. In addition, YOU said
Since it is hemipshereical, the surface area willbe half
[tex]Surface Area of hemispherical dome=2\pi(r^2)[/tex]
but then say
[tex]dSA=4\pi(r)dr[/tex]
You don't want Surface area, you want VOLUME. The volume of a sphere is [itex]\frac{4}{3}\pi r^3[/itex]. The differential is [itex]dV= \frac{4}r^2 dr[/itex] which is exactly the same as the surface area times the "thickness" dr. I thought that was what you were doing when you quoted the formula for surface area!
 

Related Threads on Linear approximation of paint

Replies
2
Views
2K
  • Last Post
Replies
3
Views
513
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
12
Views
4K
  • Last Post
Replies
4
Views
2K
Top