# 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?

Question
1 views

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?

check_circle

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 , ...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in