Question -:
A circular plate has a circumference 20.7 inches . What is the area of the plate.
Explanation -:
In this problem we are provided the circumference of the circular plate which is 20.7 inches and asked to find the area of the circular plate.
[tex] \small \underline{ \underline{\rm \purple{ {First \: we \: will \: calculate \: the \: value \: of \: r}}}}[/tex]
We know,
[tex] \orange \star \: \large \boxed{ \orange{ \rm{ Circumference_{(circle)} = 2πr}}}[/tex]
Where,
- r stand for radius
- Assuming π as 3.14
Substituting the values we get
[tex] \small\bf{ 20.7 = 2 × 3.14 × r}[/tex]
[tex] \small\rm{ \cancel\dfrac{20.7}{2} =3.14 × r}[/tex]
[tex] \rightarrow \small\rm{ 10.35 =3.14 × r}[/tex]
[tex] \rightarrow \small\rm{ \cancel \dfrac{ 10.35 }{3.14} = r} [/tex]
[tex] \small \rm \red{r \approx 3.29inches} [/tex]
[tex] \small \underline{ \underline{ \purple{\rm Now \: we \: will \: calculate \: the \: area \: of \: the \: circular \: plate}}}[/tex]
[tex] \pink\star \: \large\boxed{ \rm{ \pink{Area_{(circle)} = πr²}}}[/tex]
[tex] \small\bf{ Area_{(circle)} = 3.14 × {3.29}^{2} }[/tex]
[tex] \small\rm{ Area_{(circle)} = 3.14 × 10.82}[/tex]
[tex] \small\rm \red{{Area_{(circle)} \approx33.97inches} }[/tex]
Area of the circular plate ≈ 33.97 inches
