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Numerade Educator

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Problem 64 Hard Difficulty

Solve Example 9 taking cross-sections to be parallel to the line of intersection of the two planes.

Answer

$\frac{128}{3 \sqrt{3}}$

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Video Transcript

we know we're looking at the equation X squared plus y squared is 16. Which means if we write this in terms of acts, we get plus or minus times of sport of 16 minus y squared, which means the wet is squirt of 16 minutes Y squared, minus negative scores of 16 minus y squared. Remember, we're looking at the left of the Y axis in this context for the negative. And the positive square root is on the right side of the wax is which gives us two times squirt of 16 minus y square. No, we know our way of why is gonna be Why times 10 of 30 degrees. Which did you have? Your unit circle out, you know, is to over squirt of three times 16 minus y squared. And this was under the square root right over here. Okay, now that we have this, we know we can integrate us. So when we integrate this, we increase the exponents by one, and we divide by the new expert, and then the integration is gonna be from 0 to 4 plug in. So we're just plugging in our bounds now when we're doing the integration remember that zero plugged in is often just a zero, so be careful with that and then simplified us to get 128. Divide by three square root of three.