Name: Perimeter of a Closed Semicircular Figure
Uploaded: 2019-07-19
Duration: 2 min 24 s
Description: We know how to calculate the circumference or perimeter of a circle. Let’s watch how to calculate the perimeter of a closed semicircular figure in this video.

Question

A circular pond is surrounded by a $2 m$ wide circular path. If the outer circumference of the circular path is $44 m$ , find the inner circumference of the circular path. Also, find the area of the path. Use $π = \frac{22}{7}$ .

Accepted Answer

Given: A circular pond is surrounded by a circular path of width $2 m$ .

Also, the outer circumference of the circular path is $44 m$ .

To find:

Find the inner circumference of the circular path.

Find the area of the path.

Solution: The following figure represents the given situation

Let $R$ be radius of outer circle and $r$ be radius of inner circle.

Circumference of outer circle, $= 44 m$ ......................(Given)

$\Rightarrow 2 π R = 44 m$

$\Rightarrow 2 \times \frac{22}{7} \times R = 44 m$
$\Rightarrow R = \frac{7 \times 44}{2 \times 22} m$

$\Rightarrow R = 7 m$

From the figure, radius of inner circle, $r = (R - 2) m$ .

$\Rightarrow r = (7 - 2) m$

$\Rightarrow r = 5 m$ .

Circumference of inner circle $= 2 π r$ $= 2 \times \frac{22}{7} \times 5$ $= 31.43 m$

Hence, the inner circumference of the circular path is $31.43 m$ .

From the figure it can be observed that the area of the path will be equal to area of outer circle minus the area of the inner circle.
Therefore, area of the path $=$ area of outer circle $-$ area of inner circle

$= π R^{2} - π r^{2}$

$= π (R^{2} - r^{2})$

$= \frac{22}{7} (7^{2} - 5^{2})$

$= \frac{22}{7} \times (49 - 25)$

$= \frac{22}{7} \times 24$

$= 75.43 m^{2}$ .

Hence, the area of the circular path around the pond is $75.43 m^{2}$

A circular pond is surrounded by a $2 m$ wide circular path. If the outer circumference of the circular path is $44 m$ , find the inner circumference of the circular path. Also, find the area of the path. Use $π = \frac{22}{7}$ .

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Learn and Prepare for any exam you want !

A circular pond is surrounded by a 2 m wide circular path. If the outer circumference of the circular path is 44 m, find the inner circumference of the circular path. Also, find the area of the path. Use π=227.

Chapter-Wise 3D Mathematics Videos from NCERT NCERT Exemplar Mathematics - Class 7

Perimeter of a Closed Semicircular Figure

Perimeter of Semicircle: Illustration

Finding Area of Equilateral Triangle

Learn and Prepare for any exam you want !

A circular pond is surrounded by a $2 m$ wide circular path. If the outer circumference of the circular path is $44 m$ , find the inner circumference of the circular path. Also, find the area of the path. Use $π = \frac{22}{7}$ .