Asked Jan 16, 2020

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?


Expert Answer

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.

Calculus homework question answer, step 1, image 1
Step 2

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

Calculus homework question answer, step 2, image 1
Step 3

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

Calculus homework question answer, step 3, image 1

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