Stuck on this particular maths problem, please help?!?
The question states 'A square of side 10cm is drawn inside a circle. a) Find the diameter of the circle. b) Find the shaded area
Thanks very much!
If you draw the diagonal of the square it turns into two right angled triangles. Focus on one of those triangles. You know that two of the triangles sides are 10 cm (because it is a square with 10 cm sides and all the sides of a square are the same). You can then use Pythagoras theorem to work out the diameter of the square (because the diagonal of the square is also the diameter of the circle).
a(squared) + b(squared) = c(squared)
so: 10(squared) + 10(squared) = c(squared)
100 + 100 = c(squared)
200 = c(squared)
200(rooted) = c
c = 14.14213562 cm
THE DIAMETER OF THE CIRCLE IS 14.1 CM (TO 3 SIGNIFICANT FIGURES)
To work out the shaded area you can work out the area of the square and take it away from the area of the circle, then divide it by 4 (because you don't want the area of all 4 of the outer parts, but just 1).
area of square: 10 x 10 = 100 cm(squared)
area of circle: πr(squared)
= π x 7.071067812(squared)
= 157.0796327 cm(squared)
Area of circle - area of square = 157...-100
now you want just that one part that is shaded, so divide the answer by 4:
57.0796327/4 = 14.26990817 cm(squared)
BDW lol i had that maths book XD
Since it's a square with a side length, s, you know that the length of the square's diagonal, which is equal to the diameter of the circle, d, is:
d = s√2 = 10√2 = 14.14 cm
I'm guessing that the "shaded area" is the region inside the circle, but outside the square. The area of the circle, Ac, is:
Ac = πd2/4 = π(14.14)2/4 = 50π
The area of the square, As, is:
As = s2 = (10)2 = 100
The area of the region inside the circle, but outside the square, is:
A = Ac - As = 50π - 100 = 57.08 cm2
if you find out the diagonal of the square
that's the diameter of the circle
c=10sqrt2 = diameter
radius is 5sqrt2
hope that helps you find the area in the shaded portion