Question

If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm. (Give your answer correct to 4 decimal places.) cm/min

Answer 1

Answer:

0.0723 cm/min

Step-by-step explanation:

A snowball is spherical, so it's area is given by the following formula:

$A = 4\pi r^{2}$

The radius is half the diameter, so:

$A = 4\pi (\frac{d}{2})^{2}$

$A = \pi d^{2}$

If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.

This is $\frac{dd}{dt}$ when $\frac{dA}{dt} = -5, d = 11$

$A = \pi d^{2}$

Applying implicit differentiation:

We have to variables(A and d), so:

$\frac{dA}{dt} = 2\pi d \frac{dd}{dt}$

$-5 = 22\pi \frac{dd}{dt}$

$\frac{dd}{dt} = -\frac{5}{22\pi}$

$\frac{dd}{dt} = 0.0723$

So the answer is

0.0723 cm/min