Surface calculation(geometry)

(300 +31.5 PI) sq cm.

a=R

A=4*r^2-((4*R^2-PI*R^2)/4)+( R^2*PI/8)+(3*R^2*PI/16)

A=(3*R^2)+(1/16)*(R^2*PI)

R=10 cm

A=3*100+314/16

A=300+19.6=319.6

319.6 sq cm

Bill,

That doesn't look enough (and nor does my first answer).

Whole squares = 300
Quarter large circle = 25 PI
One and a quarter small circles = 1.25 x 25 PI =


TOTAL = 300+ 2.25 x 25 PI

=476.7375 sq cm

Fresco as you have one small circle with one half it area adding to the color area and one adding 3/4 to the color area and each of those circle are only 1/4 the area of the large circle and then you need to subtract 1/4 of the difference in area between the larger circle and the box.

So the area of the two smaller circles that add to the total color area is 98.17.

Then you have the box with an area of 400 minus plus 98.17 and minus 1/4 of 400-314 or 21.5.

S0 498.17-21.5=476.67!

Damn it you was right and I will need to go back over my general setup to find where my error or errors happen to be in the setup.

It had been decades since I had been in the habit of setting UP and solving even simple algebra base equations so some rust seem to had occur.

Thank for pointing out the error and sometime when my mind is working better I will see where I went wrong in the equations.

Found my error A=3*R^2+(9/16)*(R^2*PI) instead of the term (1/16)*(R^2*PI) or in other word I subtracted instead of added to reach that term.

The set up was ok but in solving the equation I did a simple error I should be ashame of.


a=R

A=4*r^2-((4*R^2-PI*R^2)/4)+( R^2*PI/8)+(3*R^2*PI/16)

A=(3*R^2)+(1/16)*(R^2*PI)

R=10 cm

A=3*100+314/16

A=300+19.6=319.6

319.6 sq cm