Question

Find the perimeter of a semicircle of diameter 28 cm (Take pi =22/7)

Answer 1

Given:

A semicircle of diameter 28 cm

To find:

The perimeter

Solution:

The diameter of the semicircle, d = 28 cm

∴ The radius of the semi-circle, r = $\frac{d}{2} = \frac{28}{2} = 14\:cm$

We know the formula of the perimeter of a semicircle is as follows:$\boxed{\bold{Perimeter\:of\:a\:semi-circle = [\frac{1}{2} \times Circumference\:of \:circle]+ [Diameter]}}$

Therefore, we get

$Perimeter = [\frac{1}{2}\times 2\pi r ] + d$

now, by substituting the values in the formula

$\implies Perimeter = [\frac{1}{2}\times 2\times \frac{22}{7} \times 14 ] + 28$

$\implies Perimeter = [ \frac{22}{7} \times 14 ] + 28$

$\implies Perimeter = [ 22 \times 2 ] + 28$

$\implies Perimeter = 44 + 28$

$\implies \bold{Perimeter = 72\:cm}$

Thus, the perimeter of the semi-circle is → 72 cm.

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Answer 2

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Given :-}}}}}}$

☞ Diameter of circle = 28cm

$\Large{\underline{\underline{\textsf{\maltese\: {\red{To Find :-}}}}}}$

☞ Perimeter of a semicircle ( including its diameter) = ?

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Concept Implemented :-}}}}}}$

☞ Circumference of circle (⭕) = 2πr

☞ Semi Perimeter of circle (⭕) = πr

☞ Diameter = 2 × Radius

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Solution :-}}}}}}$

» Radius = $\bf \dfrac{Diameter}{2}$

= $\sf \dfrac{28cm}{2}$

= 14cm

» Perimeter of a semicircle ( including its diameter) = Semi Perimeter of circle + Diameter

» Perimeter of a semicircle ( including its diameter)

= πr + d

= πr + 2r

= r(π + 2)

= ${14(\dfrac{22}{7} + 2 )}$cm

= ${14(\dfrac{22 \; + \; 14}{7})}$cm

= $14\; * \; \dfrac{36}{7}$ cm

= 2 × 36 cm

= 72 cm

∴ Perimeter of a semicircle ( including its diameter) $\underline{\underline{\bf{72 \:cm}}}$.