Lightyears and the surface area of a planet.

[niyati]

A light year is the unit of distance that light, with a speed of 2.99792e8 m/s, travels in one year. What is the surface area of a planet whose radius is 1300 km? Answer in units of lightyears^2.

I am wondering if my method is correct.

SA of a sphere is 4[pi]R^2. With R = 1300, the surface area is 6.76e6[pi] km^2. Since they want this number in terms of light years, I need to first, well, convert the ratio into years. With dimension analysis (not the internet), I found that there was 31536000 seconds in one year. Setting up a proportion, that's about 9.45e15 meters in one year, or 9.45e12 km in one year. I squared that number (this is the part I am most unsure about) and then divided 6.76e6[pi] by about 8.94e25 km^2, to get 2.38e-19. But I don't think that's right, because the dimensions actually cancel, then.

>_<

Help?

 

[dextercioby]

You should divide 6.76e6[pi] km^2 by 8.94e25 km^2/lighyears^2. The units will be okay.

 

[niyati]

Thank you!

I forgot about km^2 being overlightyears^2.

:D