Math, asked by vinod198710, 1 year ago

if the area of a circle increases at a uniform rate then prove that the parameter varies inversely as the radius

Answers

Answered by rahul11kapoor
0

fferentiating w.r.t t

t

on both sides we get,

dAdt=π.2r.drdt

d

A

d

t

=

π

.2

r

.

d

r

d

t

It is given that the area is increasing at a uniform rate.

∴dAdt=k⇒2πr.drdt=k

d

A

d

t

=

k

2

π

r

.

d

r

d

t

=

k

Step 2

where k

k

is a constant ∴drdt=k2πr

d

r

d

t

=

k

2

π

r

Perimeter of the circle is

p=2πr

p

=

2

π

r

Differentiatily w.r.t t

t

we get

dpdt=2π.drdt

d

p

d

t

=

2

π

.

d

r

d

t

Substituting for drdt

d

r

d

t

we get

dpdt=2π.k2πr

d

p

d

t

=

2

π

.

k

2

π

r

dpdt=kr

d

p

d

t

=

k

r

⇒dpdtα1r

d

p

d

t

α

1

r

Hence this proves that the perimeter varies inversely as the radius.

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