Answer:
a. 10cm
b. 5 cm
c. 31.4 cm
d. 78.5 cm²
e. 100 cm²
Explanation:
Let:
s - side of the square
d - diameter of the circle
r - radius of a circle
C - circumeference of the circle
AC - area of the circle
AS - area of a square
The formula of a perimeter of a square:
P = 4s
We have P = 40cm.
Substitute:
4s = 40 divide both sides by 4
s = 10 cm
a.
The length of the diameter of the circle inscribed in the square is equal to the length of the side of the square.
Therefore d = s → d = 10 cm.
b.
The length of the circle diameter is two lengths of the circle radius.
Therefore d = 2r → r = d : 2 → r = 10 : 2 = 5 cm.
c.
The formula of a circumference of a circle:
C = dπ.
Substitute d = 10cm, and π = 3.14.
C = 10(3.14) = 31.4 cm.
d.
The formula of an area of a circle:
AC = πr²
Substitute r = 5cm and π = 3.14
AC = 3.14(5²) = 3.14(25) = 78.5 cm².
e.
The formula of an area of a square:
AS = s²
Substitute s = 10 cm
AS = 10² = 100 cm²