Question

A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 5 cm per second.

Answer 1

Answer:

a) $r(t)=5t$

b) $A=\pi\cdot r^2$

c) $A=\pi\cdot (5t)^2$

d) $A=25\pi t^2$

Step-by-step explanation:

We know that the circle is increasing its radio from an initial state of r=0 cm, at a rate of 5 cm/s.

This can be expressed as:

$r(0)=0\\\\dr/dt=5\\\\r(t)=r(0)+dr/dt\cdot t=0+5t\\\\r(t)=5t$

a) Radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing:

$r(t)=5t$

b) Area of the circle, A (in square cm), in terms of the circle's radius, r (in cm):

$A=\pi\cdot r^2$

c) Circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing:

$A=\pi\cdot r^2\\\\A=\pi\cdot (5t)^2$

d) Expanded form for the area A:

$A=\pi\cdot (5t)^2=25\pi\cdot t^2$