Question

If the circumference of a circular sheet is 176m ,find its diameter and area.​

Answer 1

Answer:

           diameter = 56m

                   area = 4928m²

Step-by-step explanation:

circumference of circle - 2πr

176m = 2πr

176 = 2 × 22/7 × r

r = 176 × 7 / 22 × 2

r = 1232 / 44

r = 28m

diameter - d = 2r = 56m

area = πr²

= 2 × 22/7 × 28 × 28

= 2 × 22 × 4 × 28

= 4928m²

Answer 2

Answer -

• The diameter of the circular sheet = 28 m.

• The area of the circular sheet = 2464 m².

To find -

• The diameter and area of the circular sheet.

Step-by-step explanation -

• Here, the circumference of a circular sheet is given to us. We have to find it's diameter and area. So first we will find the radius of the sheet using the circumference and later use it to find it's diameter and area!

We know that -

$\bigstar \: \underline{\boxed{\sf Circumference_{(circle)} = 2 \pi r}}$

Where -

• r = Radius.

Here -

• Circumference = 176 m.
• π = 22/7.

Let -

• The radius of the circular sheet be "r" m.

Substituting the given values in this formula -

$\implies\tt176 = 2 \times \dfrac{22}{7} \times r$

$\implies\tt176 = \dfrac{44}{7} \times r$

$\implies \tt176 = \dfrac{44r}{7}$

$\implies \tt176 \times 7 = 44r$

$\implies \tt1232 = 44r$

$\implies \tt \cancel{\dfrac{1232}{44}} = r$

$\implies \tt{28 \: m = r}$

Hence -

• The radius of the circular sheet is 28 m.

------------------------------------

• Let's find the diameter of the circular sheet now!

We know that -

$\bigstar \: \underline{\boxed{\sf Diameter_{(circle)} = 2 \times r}}$

Where -

• r = Radius.

Here -

• Radius = 28 m.

Therefore -

$\bf \hookrightarrow Diameter = 2 \times 28$

$\bf \hookrightarrow Diameter = 56 \: m$

Hence -

• The diameter of the circular sheet is 56 m.

________________________________

• Finally, let's find the area of the circular sheet!

We know that -

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

Where -

• r = Radius.

Here -

• Radius = 28 m.

Therefore -

$\longmapsto \rm Area = \dfrac{22}{7} \times {28}^{2}$

$\longmapsto \rm Area = \dfrac{22}{7} \times 784$

$\rm \longmapsto Area = \cancel{\dfrac{17248}{7}}$

$\rm \longmapsto Area = 2464 \: {m}^{2}$

Hence -

• The area of the circular sheet is 2464 m².

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