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## Homework Statement

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

## Homework Equations

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.