Question

heyy guys
Provide me with the correct solution for this question​

Answer 1

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

The perimeter of a sector of circle with central angle 90° is 25cm.Find the area of the minor segment.

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

Given:

• Central angle of a sector = 90°.
• Perimeter = 25cm.

To find:

• The area of minor sector.

Solution:

We know,

✦For a whole circle,the central angle is 360°

✦∴One-fourth of a circle is 90°

✦Perimeter of a circle is the circumference.

$\leadsto \underline{\boxed{\sf Perimeter \ of\ circle =2\pi r}}$

Therefore,

$\leadsto \underline{\boxed{\sf Perimeter\ of\ sector=\frac{1}{4} (perimeter\ of\ circle) }}$

Substituting the values,

$:\implies \sf 25=\frac{1}{4} (2\pi r)\\\\:\implies \sf 100=2\pi r\\\\:\implies \sf \frac{100}{2\pi } = r\\\\:\implies \bold{r=\frac{50}{\pi } }$

Also,

$\leadsto \underline{\boxed{\sf Area\ of\ minor\ segment=\frac{1}{4} (Area\ of \ circle) }}$

$\leadsto \underline{\boxed{\sf Area\ of\ circle=\pi r^2 }}$

Now,

$:\implies \sf Area \ of\ minor\ segment =\frac{1}{4} (\pi r^2 )\\\\:\implies \sf \frac{1}{4} \times \pi \times (\frac{50}{\pi } )^2\\\\:\implies \frac{2500}{4\pi } =\frac{625}{\pi }$

[π=3.14]

$:\implies \sf \frac{625}{\pi } \\\\:\implies \sf \frac{625}{3.14} \\\\:\implies \sf 199.04cm^2.\\\\\\\therefore \boxed{\boxed{\sf Area\ of\ minor\ segment=199.04cm^2.}}$

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

Know More:-

Area of a Segment in Radians.

• A = (½) × r2 (θ – Sin θ)

Area of a Segment in Degrees.

• A = (½) × r 2 × [(π/180) θ – sin θ]

Ar.(segment) = Ar.(sector) - Ar.(triangle)

______________

Answer 2

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

The perimeter of a sector of circle with central angle 90° is 25cm.Find the area of the minor segment.

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

Given:

Central angle of a sector = 90°.

Perimeter = 25cm.

To find:

The area of minor sector.

Solution:

We know,

✦For a whole circle,the central angle is 360°

✦∴One-fourth of a circle is 90°

✦Perimeter of a circle is the circumference.

$\leadsto \underline{\boxed{\sf Perimeter \ of\ circle =2\pi r}}$

Therefore,

$\leadsto \underline{\boxed{\sf Perimeter\ of\ sector=\frac{1}{4} (perimeter\ of\ circle) }}$

Substituting the values,

$:\implies \sf 25=\frac{1}{4} (2\pi r)\\\\:\implies \sf 100=2\pi r\\\\:\implies \sf \frac{100}{2\pi } = r\\\\:\implies \bold{r=\frac{50}{\pi } }$

Also,

$\leadsto \underline{\boxed{\sf Area\ of\ minor\ segment=\frac{1}{4} (Area\ of \ circle) }}$

$\leadsto \underline{\boxed{\sf Area\ of\ circle=\pi r^2 }}$

Now,

$:\implies \sf Area \ of\ minor\ segment =\frac{1}{4} (\pi r^2 )\\\\:\implies \sf \frac{1}{4} \times \pi \times (\frac{50}{\pi } )^2\\\\:\implies \frac{2500}{4\pi } =\frac{625}{\pi }$

[π=3.14]

$:\implies \sf \frac{625}{\pi } \\\\:\implies \sf \frac{625}{3.14} \\\\:\implies \sf 199.04cm^2.\\\\\\\therefore \boxed{\boxed{\sf Area\ of\ minor\ segment=199.04cm^2.}}$

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

Know More:-

Area of a Segment in Radians.

A = (½) × r2 (θ – Sin θ)

Area of a Segment in Degrees.

A = (½) × r 2 × [(π/180) θ – sin θ]

Ar.(segment) = Ar.(sector) - Ar.(triangle)

______________