Assume that the Earth is a sphere with circumference of 24,900 miles.
a. Find the volume of the Earth north of latitude 45 degrees. (hint: integrate with respect to y)
b. Find the volume of the Earth between the equator and latitude 45
circle: x^2 + y^2 = r^2
The Attempt at a Solution
so far, I have just been working on A. I took a cross section of the sphere from latitude 45 and up and drew it on a graph. I realized that if i revolved it around the y-axis that it would form the shape I need, a dome.
I found the radius using the circumference and set up my integral.
i have: pi * int(124500pi - y^2 dy after simplifying.
I think i'm all set to integrate and find the answer, but I cant figure out what to use for the upper and lower bounds. I thought i might try and use sin(45) or cos(45) or tan(45), in some way, but I cant really wrap my head around the problem from this point forward.