Question

Water slowly evaporates from a circular shaped puddle. The radius of the puddle decreases at a rate of 7 in/hr. Assuming the puddle retains its circular shape, at what rate is the area of the puddle changing when the radius is 3 in?

Answer 1

You will need a formula for the area of a circle.
You will need a derivative, in differential form.
You are almost done.

Answer 2

\[A=\pi r^2\]

Answer 3

the derivative of the area formula?

Answer 4

A is 2

Answer 5

wait why?

Answer 6

@Mrs.ambrose614

Answer 7

\(A = \pi r^{2}\)

Differential Form of the Derivative

\(dA = 2\pi r\;dr\)

Fill in the blanks.

Answer 8

A =2

Answer 9

\[dA=-42\pi\]

Answer 10

is that the answer?

Answer 11

No, that can't be the answer. Find your units and show your work.

Good call. It SHOULD be negative, since it's shrinking.

Answer 12

\[dA=2\pi r *dr\]
\[dA=2\pi(3)*(-7)\]
\[dA=-42\pi\]

Answer 13

This is what I did

Answer 14

Well, that looks fine from a purely numerical point of view. Still needs units. Units will save you.

Answer 15

oh so \[42\pi m^2/hr\]

Answer 16

in not m sorry

Answer 17

\(2\cdot\pi\cdot (3\;in)\cdot \dfrac{7\;in}{hr} = -42\pi\;in^2/hr\)