Question

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
a) 0.7 cm/s
b) 1.4 cm/s
c) 2.1 cm/s
d) 0.35 cm/s

Answer 1

Answer: B. 1.4π cm/s

Step-by-step explanation:

This is a related rates problem, meaning that we must use the circumference formula and the information given to us, derive the equation and substitute the values to get our answer.

Circumference of a circle Equation: $\[\boxed{C = 2\pi r}\]$

Let's derive this equation and solve.

Solving:

${C = 2\pi r}$ ⇒ Differentiate this in terms of time

$\[ \frac{dC}{dt} = \frac{d}{dt}(2\pi r) \]$

$\[ \frac{dC}{dt} = 2\pi \frac{dr}{dt} \]$

Now plug in 0.7 cm/s in for dr/dt(change in radius in respect to time)

$\[ \frac{dC}{dt} = 2\pi \times 0.7 = 1.4\pi \]$

Which means that Option B is the correct answer

That's it!

Answer 2

Final answer:

The rate of the circumference increase of a circle with a radius increasing at 0.7 cm/s is b.1.4 cm/s.

Explanation:

The rate of increase of the circumference of a circle can be calculated using the formula:

Circumference rate = (rate of change of radius) * (2 * π)

Given that the radius is increasing at 0.7 cm/s, the rate of increase of the circumference is:

Circumference rate = 0.7 * 2 * π = 1.4 cm/s