Question

a circle has an area of 78mm^2. find its diameter

Answer 1

use the formula, insert the values and Bingo!

Answer 2

try it..

Answer 3

\[\pi (r)^2 = 78\]

Answer 4

Remember the formula A=(pi)r^2. Well you want to find the diameter d which is related to r by: d=2r. Therefore r = d/2. Substitute this into the Area formula for r to get:

A = (pi)(d/2)^2 = (pi)d^2/4. Now rearrange this to get d in terms of A and pi:

d = [4A/(pi)]^(1/2) and take the positive root.

Answer 5

Now just plug in your value for A to get the diameter in mm^2

Answer 6

this formula is complicated can you write in a simple way

Answer 7

\[A = \pi (d/2)^2 = \pi d^2 / 4\]

Answer 8

Next I just re-arranged to find \[d \] in terms of \[\pi \]. You do this by writing:

Answer 9

\[d = [4A/(\pi)]^{1/2} = \sqrt{4A/(\pi)}\]

Answer 10

can you check I got 25.8 is that right

Answer 11

24