Note: the diameter is always twice as much the radius
1) r = 13cm
2) d = 27.2in
3) d = 24x
4) r = 24.5m
5) There is a circle inside a square, so the side of the square (16in), corresponds to the diameter of the circle.
radius = 8in
area = (pi)r^2 = 3.14 (8in)^2 = 3.14 (64in^2) = 200.96in^2
Circumference = 2(pi)r = 2(3.14)8in = 50.24in
6) The hypotenuse of the right triangle inside the circle is equal to the diameter of the circle. So we need to find it using the Pythagorean theorem.
d^2 = (10^2 + 24^2)cm
d^2 = (100 + 576)cm
d^2 = (676)cm
d = 26cm
So, radius = 13cm
Area = (pi)r^2 = 3.14 (13cm)^2 = 3.14 (169cm^2) = 530.66cm^2
Circumference = 2(pi)r = 2(3.14)(13cm) = 81.64cm
7) The diagonal of the square is equal to the diameter of the circle, so we need to find it using a formula.
d =[sqrt(2)] (5in)
I won’t calculate it now, because it’s a periodic number.
r = {[sqrt(2)] (5in)} : 2
Area = (pi)r^2 = 3.14 {[sqrt(2)(5in)]:2}^2 = 3.14 (12.5in^2)= 39.25in^2
Circumference = 2(pi)r = 2(3.14)(12.5in) = 78.5in
8) If a right triangle has two equal sides, it means that it is half of a square.
So we can apply the same formula as before.
d =[sqrt(2)] (8)
I won’t calculate it now, because it’s a periodic number.
r = {[sqrt(2)](8)}:2
Area = (pi)r^2 = 3.14 {[sqrt(2)(8)]:2}^2 = 3.14 (32) = 100.48
Circumference = 2(pi)r = 2(3.14)(32) = 200.86
{there aren’t units of measurement in this exercise}
I hope there are no accidental errors. :)