Calculating Radius of Circular Area from Laser Power and Energy Density

[Dart82]

Homework Statement

energy density in a laser beam is 9.5x10^-8 J/m cubed. the laser beam is cylindrical, and it delivers a power of 15W to a certain area. What is the radius of this circular area?

Homework Equations

Intensity :
S=cu and S=Power/Area
Area of a circle (or possibly the area of a cylinder?)

The Attempt at a Solution

first i find the intensity by multiplying the speed of light by the energy density in the laser: (2.994x10^8)x(9.5x10^-8)=28.44
Then i find the Area using S=P/A: 28.44/15W=1.89m
Using the area of a circle: 1.89=pi*radius^2. According to my calculations, my radius would be .78 meters. The correct answer is supposed to be 0.41 meters. Can someone please tell me where i am screwing this one up

 

[hage567]

Homework Statement

energy density in a laser beam is 9.5x10^-8 J/m cubed. the laser beam is cylindrical, and it delivers a power of 15W to a certain area. What is the radius of this circular area?

Homework Equations

Intensity :
S=cu and S=Power/Area
Area of a circle (or possibly the area of a cylinder?)

The Attempt at a Solution

first i find the intensity by multiplying the speed of light by the energy density in the laser: (2.994x10^8)x(9.5x10^-8)=28.44
Then i find the Area using S=P/A: 28.44/15W=1.89m
Using the area of a circle: 1.89=pi*radius^2. According to my calculations, my radius would be .78 meters. The correct answer is supposed to be 0.41 meters. Can someone please tell me where i am screwing this one up

You made a math error. You accidently calculated S/P for the area, when it should be P/S. So it should be 15W/28.44 instead of what you have.

 

[Dart82]

ohhhhh...that would seem to be a problem. thanks!