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?

Answer 1

\[\LARGE C= 2 \pi R \]
\[\LARGE \frac{dC}{dt}=2 \pi \frac{dR}{dt}=2 \pi \times 0.7\]
is this correct?

Answer 2

2pi*dr/dt

Answer 3

looks like ur right

Answer 4

to be exact

Answer 5

1.4pi ceminiters

Answer 6

or 2pi(0.7)

Answer 7

but the solution says
\[\LARGE \frac{dC}{dt}=\frac{dC}{dR} \times \frac{dR}{dt}\]
why is it so? though answer is same

Answer 8

how do i post pictures?

Answer 9

attach file/draw

Answer 10

That's just the chain rule. Are you asking for a proof of the rule, or why they wrote the answer that way?

Answer 11

latter!

Answer 12

i mean simply what i wrote in first line is wrong?

Answer 13

No, it's not wrong. Their statement is more general, yours is specific to the question, but they're both right.

Answer 14

The circumference of a circle (C) with radius (r) is given by
C = 2πr.
Therefore, the rate of change of circumference (C) with respect to time (t) is given by,

Answer 15

ur welcome

Answer 16

i got it now :D thanks