Question

if the circumference of a circular sheet is 154 m, find its radius. Also find the area of the
sheet.​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Answer:}} }} }$

✰ Radius of the circular sheet is 24.5 m.

✰ Area of the circular sheet is $\rm { 1886.5 \: {m}^{2}}$.

$\underline{ \underline{ \Large \pmb{\sf { {Given:}} }} }$

• Circumference of the circular sheet = 154 m

$\underline{ \underline{ \Large \pmb{\sf {{To \: calculate:}} }} }$

• Radius of the circular sheet.

• Area of thr circular sheet.

$\underline{ \underline{ \Large \pmb{\sf {{Calculation:}} }} }$

Here, as per the given question we have been given the circumference of the circle. So, by using the formula of the circumference of the circle, we'll find the measure of radius. After finding radius, we'll substitute the value of radius in the formula of the area of the circle to find the area of the circular sheet.

⠀⠀⠀⠀⠀_____________

Let the radius of the circular sheet be "r".

According to the question,

$\longrightarrow \sf { Circumference = 154 \: m}$

We know that, circumference = 2πr. So,

$\longrightarrow \sf { 2 \pi r = 154 } \\ \\ \\ \longrightarrow \sf { \pi r = \dfrac{154}{2} } \\ \\ \\ \longrightarrow \sf { \pi r = 77 } \\ \\ \\\longrightarrow \sf { \dfrac{22}{7} r = 77 } \\ \\ \\\longrightarrow \sf { r = 77 \times \dfrac{7}{22} } \\ \\ \\\longrightarrow \sf { r = 7 \times \dfrac{7}{2} } \\ \\ \\ \longrightarrow \sf { r = \dfrac{49}{2} }\\ \\ \\ \longrightarrow \boxed{ \pmb{ \sf { r = 24.5 \: m }} }$

Henceforth,

• Radius of the circular sheet is 24.5 m.

» Now, let's calculate its area.

We know that,

$\longrightarrow \: \bigstar \boxed{ \sf { Area_{(Circle)} = \pi {r}^{2} }}$

Substituting values, we get :

$\longrightarrow \sf { Area_{(Circle)} = \dfrac{22}{7} \times {24.5}^{2} } \\ \\ \\ \longrightarrow \sf { Area_{(Circle)} = \dfrac{22}{\cancel {7}} \times \cancel{24.5} \times 24.5 } \\ \\ \\ \longrightarrow \sf { Area_{(Circle)} = 22 \times 3.5 \times 24.5 } \\ \\ \\\longrightarrow \sf {Area_{(Circle)} = 22 \times \dfrac{35 }{10} \times \dfrac{245}{10} } \\ \\ \\\longrightarrow \sf { Area_{(Circle)} = 22 \times \dfrac{7}{2} \times \dfrac{245}{10} } \\ \\ \\ \longrightarrow \sf { Area_{(Circle)} = 11 \times 7 \times \dfrac{245}{10} } \\ \\ \\ \longrightarrow \sf { Area_{(Circle)} = \dfrac{18865}{10} }\\ \\ \\ \longrightarrow \boxed{ \pmb{ \sf { Area_{(Circle)} = 1886.5 \: {m}^{2}}} }$

Therefore,

• Area of the circular sheet is $\rm { 1886.5 \: {m}^{2}}$.