A schematic drawing of an 82 foot Dome used by a Weather Service to house radar as shown to the right. So the fact that it's a Dome note, we know that the equation is going to be a circle X ^2 + y ^2 equal 41 ^2, and we're going to be going around the Y axis. So we're going to integrate in terms of DY, we're going to have X equaling sqrt 41 ^2 -, y ^2. Our DXDY is going to be -2 Y over two square roots of 41 ^2 -, y ^2. And that's just really negative Y over square root 41 ^2 -, y ^2. So we're going to go from -20.5 to 41 based on our picture, thinking about that center being our origin, 2π our radius. Remember our radius is how far over we go each time. So our radius is going to be the X. In this case, our X is sqrt 41 ^2 -, y ^2 * sqrt 1 + d XD y ^2 d Y. Getting a common denominator underneath the square root, we're going to get 41 ^2 - y ^2 + y ^2. So the Y squareds are going to cancel sqrt 41 ^2 -, y ^2 is also going to cancel top and bottom. So we're going to get left sqrt 41 ^2 or 41. So 2 * π * 41 is going to give me 82π. The integration of DY is going to give us Y. So we're going to stick in our upper bound minus our lower bound and get 5043 Pi square feet. And when we plug that into our calculator, it's approximately 15,843 square feet.