Answer:
(a) 9800π cm²/s
(b) 39200π cm²/s
(c) 58800π cm²/s
Step-by-step explanation:
As we know,
The area of circle is:
[tex]A= \pi r^2[/tex]
[tex]\frac{dA}{dt}=2 \pi r\frac{dr}{dt}[/tex]
The given value is:
[tex]\frac{dr}{dt} =70 \ cm/s[/tex]
Now,
(a)
After 1 second,
r = 70×1
= 70 cm
⇒ [tex]\frac{dA}{dt}=2\pi(70)\times (70)[/tex]
[tex]=9800 \pi \ cm^2/s[/tex]
(b)
After 2 second,
r = 70×4
= 280 cm
⇒ [tex]\frac{dA}{dt}=2\pi \ (280)\times (70)[/tex]
[tex]39200\pi \ cm^2/s[/tex]
(c)
After 6 seconds,
r = 70×6
= 420 cm
⇒ [tex]\frac{dA}{dt}=2\pi \ (420)\times (70)[/tex]
[tex]58800\pi \ cm^2/s[/tex]
The rate will be:
(a) 9800 π cm²/s
(b) 39200 π cm²/s
(c) 58800 π cm²/s
A circle seems to be a closed object or structure generated by tracing a point that travels together in plane at quite a constant distances from either a specific location.
According to the question,
Speed, [tex]\frac{dr}{dt}[/tex] = 70 cm/s
We know,
The area of circle:
→ A = πr²
[tex]\frac{dA}{dt}[/tex] = 2πr[tex]\frac{dr}{dt}[/tex]
(a) After 1 s, the rate be:
r = 70 × 1
= 70 cm
[tex]\frac{dA}{dt}[/tex] = 2π(70) × 70
= 9800 π cm²/s
(b) After 2 s, the rate be:
r = 70 × 4
= 280 cm
[tex]\frac{dA}{dt}[/tex] = 2π(280) × 70
= 39200 π cm²/s
(c) After 6 s, the rate be:
r = 70 × 6
= 420 cm
[tex]\frac{dA}{dt}[/tex] = 2π(420) × 70
= 58800 π cm²/s
Thus the response above is correct.
Find out more information about area of circle here:
https://brainly.com/question/12069107
