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Sagot :
Given:-
[tex]\rightarrow[/tex] Side of square = 5.5 units.
[tex]\rightarrow[/tex] Circumference of circle = perimeter of square.
To Find:-
[tex]\rightarrow[/tex] Area of circle.
Solution:-
[tex]\rightarrow[/tex] To find the area of circle firstly we have to find the perimeter of the square, then we will find the radius of circle and after that area of circle. So, let's begin:
[tex]\rightarrow[/tex] Perimeter of square = [tex]\sf{4×side}[/tex](putting the value of side from the above given)
[tex]\rightarrow[/tex] [tex]\sf{=\: 4 × 5.5}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\: 22units.}[/tex]
Therefore, perimeter of square = 22units.
Now, according to the question, perimeter of square = circumference of the circle. So, circumference of circle = 22units.
Now, using the formula of circumference of circle we can find the radius.
[tex]\rightarrow[/tex] Circumference of circle = [tex]\sf{2πr}[/tex](putting the value of perimeter)
[tex]\rightarrow[/tex] [tex]\sf{22\:=\: 2×3.14×r}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{22\:=\: 6.28×r}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{22}{6.28}\:=\: r}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{3.50units\:=\: r}[/tex]
Therefore, radius of circle = 3.50units.
Now, let's find area of the circle:
[tex]\rightarrow[/tex] Area of circle = [tex]\sf{πr^2}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{πr^2}[/tex](putting the value of pie(π) and radius(r))
[tex]\rightarrow[/tex] [tex]\sf{3.14×3.50^2}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{3.14×12.25}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{38.46unit^2}[/tex]
Therefore, area of circle = [tex]\sf{38.46unit^2}[/tex]
The correct Question :-
A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for square root, and round your answer to the nearest hundredth.
Answer:-
38.47 square units
Step-by-step explanation:
All we have to do is first find the perimeter of the square (which is equal to the circumference of the circle), then find the radius of the circle and finally the area of the circle.
The square has a side that measures 5.5 units.
The perimeter of a square is given as:
- P = 4L
where L = length of side of the square
Therefore, the perimeter of the square is:
P = 4 × 5.5 = 22 units.
This means that the circumference of the circle is 22 units.
The circumference of a circle is given as:
C = 2πR
and the area of a circle is given as:
A = πr²
where R = radius
Therefore:
22 = 2πR
= R = 22 / (2 × 3.14)
R = 22 / (6.28)
R = 3.50 units
The area is therefore:
A = 3.14×3.50²
A = 38.47 square units
The area of the circle is 38.47 square units.
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