Question

the circumference of circle is 88 find the area
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Answer 1

Given Information :

• Circumference of circle = 88 units

To calculate :

• Area of the circle

Solution :

As we know that,

$\bigstar \boxed{\red{\sf{ C = 2\pi r}}}$

• C denotes circumference
• r denotes radius

$\implies\sf { 88 \; units = 2 \times \dfrac{22}{7} \times r}$

$\implies\sf { 88 \; units = \dfrac{44}{7} \times r}$

$\implies\sf { \cancel{88} \times \dfrac{7}{\cancel{44}} \; units = r}$

$\implies\sf { 2 \times \dfrac{7}{1} \; units = r}$

$\implies\boxed{\red{\sf{ 14\; units = r}}}$

Now, as we know that :

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

Substitute the values.

$\implies\sf { Area = \Bigg \{ \dfrac{22}{7} \times (14)^2 \Bigg \} \; units^2 }$

$\implies\sf { Area = \Bigg \{ \dfrac{22}{7} \times 196 \Bigg \} \; units^2 }$

$\implies\sf { Area = \Bigg \{ \dfrac{22}{1} \times 28 \Bigg \} \; units^2 }$

$\implies\boxed{\red{\sf{Area = 616 \; units^2 }}}$

∴ The area of the circle is 616 square units.

$\rule{200}2$

Answer 2

Given :

• Circumference of circle = 88 units

To Find :

• Area of the circle.

Concept :

~As per the given question we have that, Circumference of a circle is 88 units. We need to find out the area of it. For this firstly will have to find the radius of the circle using the formula of a circumference of a circle. After, finding radius we can simply use the formula of area of a circle.

Formulae Used :

$\\ \longrightarrow \boxed{ \bf \: Circumference_{(Circle)} = 2\pi r}$

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

Where,

• r = radius
• π = 22/7 or 3.14

Solution :

~Keeping all these things in mind let's start :D!

As we know that,

$\\ \longrightarrow { \bf \: Circumference_{(Circle)} = 2\pi r}$

Substituting the values we get,

$\\ \sf \longrightarrow88 \: units = 2\pi r \\ \\ \longrightarrow \sf \dfrac{88}{2} = \dfrac{22}{7} \times r \\ \\ \longrightarrow \sf \cancel\dfrac{88}{2} = \dfrac{22}{7} \times r \\ \\ \longrightarrow \sf 44 = \dfrac{22}{7} \times r \\ \\ \longrightarrow\sf 44 \times \dfrac{7}{22} = r \\ \\ \longrightarrow\sf \cancel{44 } \times \dfrac{7}{ \cancel{22}} = r \\ \\ \longrightarrow\sf 2 \times 7 = r \\ \\ \longrightarrow \underline{\underline{\bf 14 \: units = r}}$

Thus, the radius is 14 units.!

Now, as we know that,

$\\ \longrightarrow { \bf \: Area_{(Circle)} = \pi {r}^{2} }$

Substituting the values,

$\\ \sf \longrightarrow \: Area_{Circle} = \dfrac{22}{7} \times 14 \times 14 \\ \\ \sf \longrightarrow \: Area_{Circle} = \dfrac{22}{ \cancel7} \times \cancel{14} \times 14 \\ \\ \sf \longrightarrow \: Area_{Circle} = 22 \times 2 \times 14 \\ \\ \longrightarrow \sf\: Area_{Circle} = 44 \times 14 \\ \\ \longrightarrow \: \red{\boxed{ \bf \: Area_{Circle} = 616 \: {units}^{2} }}$

∴ The area of the circle is 616 units².