Find the volume of the solid in the first octant bounded by the cylinder z=16

Brittney Lord

Brittney Lord

Answered question

2021-09-17

Find the solid's first octant's volume, which is enclosed by the cylinder z=16x2 and the plane y=5

Answer & Explanation

broliY

broliY

Skilled2021-09-18Added 97 answers

Setting up the boundaries of the double integral correctly is crucial for solving this. The cylinder we are given intersects the zy plane at the line denoted by the equation x = 4 as the first thing to note. Hence our boundaries of the integral with respect to z is the segment [0, 4] Since the other plane is y = 5 by the similar reasoning we deduce y[0,5]. Finally, we integrate: 
050416x2 dx  dy =50416x2 dx =6403 
Result: 
6403

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