The radius of the circle is increasing uniformly at the rate of 3cm per second . At what rate is the area increasing when the radius is 10cms
Answers
Answered by
8
Answer:
60π cm2/sec
Step-by-step explanation:
let area A and radius r=10 cm
rate of change of radis
dr/dt= 3 cm/sec-----------(1)
==================
A=πr²
dA/dr=d/dr(πr²)
=π(2r)=2πr
dA/dr=2πr--------------(2)
Now dA/dt=dA/dr*dr/dt
=2πr*3
dA/dt=6πr
=6π*10
dA/dt=60π cm2/sec
Hence rate is of area increasing =60π cm2/sec
Answered by
0
Answer:
60πcm
Step-by-step explanation:
The area of a circle (A) with radius (r) is given by,
A=πr
2
dt
dA
=
dt
d
(πr
2
)⋅
dt
dr
=2πr
dt
dr
, [By chain rule]
It is given that,
dt
dr
=3cm/s.
∴
dt
dA
=2πr(3)=6πr
Thus, when r=10cm,
∴
dt
dA
=6π(10)=60πcm
2
/s
Similar questions