Question

If the circumference of a circular sheet is 154 m . Find it's radius And area of the sheet (take π=22/7)​

Answer 1

$\bigstar \underline{\underline{\sf Given:-}}$

• Circumference of a circular sheet =154cm.

$\bigstar \underline{\underline{\sf To\ find:-}}$

• Radius.
• Area of sheet.

$\bigstar \underline{\underline{\sf Solution:-}}$

1.To find Radius:-

We know:

✦Circumference of a sphere =2πr

Given,circumference =2πr

$:\implies \sf 2\pi r=154\\\\:\implies \sf 2(\frac{22}{7} )(r)=154\\\\:\implies \sf r=154 (\frac{7}{44} )\\\\:\implies \sf r=7(\frac{7}{2} )\\\\:\implies \sf r=\frac{49}{2} \\\\:\implies \boxed{\boxed{\sf r=24.5m.}}$

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2.To find Area of sheet:-

We know:

✦Area of sphere=πr²

$:\implies \sf Area=\pi r^2\\\\:\implies \sf \pi r^2=\frac{22}{7} (24.5)^2\\\\:\implies \sf \frac{22}{7} (\frac{49}{2} )(\frac{49}{2} )\\\\:\implies \sf 11\times \frac{343}{2} \\\\:\implies \sf \frac{3773}{2} \\\\:\implies \boxed{\boxed{\sf Area=1886.5m^2}}$

Hence,

Radius of sheet = 24.5m.

Area of sheet = 1886.5m²

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Know More:-

↬Radius =Diameter/2

↬Length of an arc =(Central angle made by the arc/360°) × 2 × π × R.

↬Equal chords and equal circles have the equal circumference.

↬Circles having different radius are similar.

↬The diameter of a circle is the longest chord of a circle.

↬Area of circle =πr².

• Area of square=(side)².

• Area of rectangle =l×b.

• Area of triangle =1/2×b×h

• Area of semi-circle: πr²/2

↬Perimeter of semi-circle: πr.

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Answer 2

$\bigstar\bf\underline{\underline{Given:-}}$

• circumference of a circular sheet is 154 m

$\bigstar\bf\underline{\underline{To \ find:-}}$

• Area of sheet

• Radius

$\bigstar\bf\underline{\underline{Solution:-}}$

Radius = r = ?

Given,

Circumference = 154m

$\sf 2\pi r \ = \ 154$

$\implies\sf 2\times \frac{22}{7}\times r \ = \ 154$

$\implies\sf \frac{2\times 22}{7}\times r \ = \ 154$

$\implies\sf r \ = \ 154\times \frac{7}{2\times 22}$

$\implies\sf r \ = \ 77\times \frac{7}{22}$

$\implies\sf r \ =  \ 7\times \frac{7}{22}$

$\implies\sf r \ = \ \frac{49}{2}$

$\boxed{\boxed{\bf Radius \ = \ 24.5m}}$

Now,

Area of circle = πr²

$\implies\sf \frac{22}{7}\times (24.5)^2$

$\implies\sf \frac{22}{7}\times (\frac{49}{2})^2$

$\implies\sf \frac{22}{7}\times \frac{49}{2}\times \frac{49}{2}$

$\implies\sf \frac{11}{7}\times 49\times \frac{49}{2}$

$\implies\sf 11\times 7\times \frac{49}{2}$

$\implies\sf 11\times \frac{343}{2}$

$\implies\sf \frac{3773}{2}$

$\boxed{\boxed{\bf 1886.5 m^2}}$

Therefore,

Radius of circular sheet is $\bf 24.5m$

Area of circular sheet is $\bf 1886.5 m^2$