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A solid rod of radius 1 cm is placed in a pipe of radius 3 cm so that their axes are aligned. Water flows through the pipe and around the rod. Find the flow rate if the velocity of the water is given by the radial function v(r) = 0.5(r − 1)(3 − r) cm/s.

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velocity of water&nbsp; v(r) = 0.5(r &minus; 1)(3 &minus; r) cm/s.
flow rate is given as,
<img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/54d13199-62fd-4ba1-81e8-19df28cddf83/25d9bbcf-82d3-4408-b704-5c4adcfc65fa/m9r09sds.png" alt="Calculus homework question answer, step 1, image 1" />

Limits for r would be from 1 to 3
<img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/54d13199-62fd-4ba1-81e8-19df28cddf83/25d9bbcf-82d3-4408-b704-5c4adcfc65fa/kc8efvb.png" alt="Calculus homework question answer, step 2, image 1" />
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Calculus

Math

A solid rod of radius 1 cm is placed in a pipe of radius 3 cm so that their axes are aligned. Water flows through the pipe and around the rod. Find the flow rate if the velocity of the water is given by the radial function v(r) = 0.5(r − 1)(3 − r) cm/s.

A solid rod of radius 1 cm is placed in a pipe of radius 3 cm so that their axes are aligned. Water flows through the pipe and around the rod. Find the flow rate if the velocity of the water is given by the radial function v(r) = 0.5(r − 1)(3 − r) cm/s.

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