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CalculusQ&A LibraryThe total surface area S of a right cir-cular cylinder is related to the base radius r and height h by the equation S = 2pai r2 + 2pai rh.a. How is dS/dt related to dr/dt if h is constant?b. How is dS/dt related to dh/dt if r is constant?c. How is dS/dt related to dr/dt and dh/dt if neither r nor h is constant?d. How is dr/dt related to dh/dt if S is constant?Question

Asked Jan 16, 2020

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The total surface area S of a right cir-cular cylinder is related to the base radius r and height h by the equation S = 2pai r2 + 2pai rh.

a. How is dS/dt related to dr/dt if h is constant?

b. How is dS/dt related to dh/dt if r is constant?

c. How is dS/dt related to dr/dt and dh/dt if neither r nor h is constant?

d. How is dr/dt related to dh/dt if S is constant?

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

Differentiate both sides with respect to t.

Step 2

#a) If h is constant then dh/dt=0 , plug this in the equation 1.

Step 3

#b) If r is constant then dr/dt=0 , ...

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