Question

The area of a semicircle is 1925 cm2. Calculate its perimeter (in cm).

A) 360 B) 80 C) 160 D) 180

Answer 1

Given :

• Area of the semi-circle is 1925 cm².

To find :

• Perimeter of the semi-circle.

Solution :

Consider,

• Radius of the semi-circle = r cm.

Formula Used :-

${\boxed{\large{\bold{Area\:of\: semicircle=\dfrac{\pi\:r^2}{2}}}}}$

According to the question :-

$\to\sf{\dfrac{\pi\:r^2}{2}=1925}$

$\to\sf{\pi\:r^2=1925\times\:2}$

$\to\sf{\pi\:r^2=3850}$

$\to\sf{\dfrac{22}{7}\times\:r^2=3850}$

$\to\sf{r^2=3850\times\dfrac{7}{22}}$

$\to\sf{r^2=1225}$

$\to\sf{r=\sqrt{1225}}$

$\to\sf{r=35}$

• Radius of the semi-circle = 35 cm.

Formula Used :-

${\boxed{\large{\bold{Perimeter\:of\: semicircle=\pi\:r+2r}}}}$

Perimeter of the semi-circle,

→ πr + 2r

→ 22/7 × 35 + 2 ×35 cm

→ 22 × 5 +70

→ 180 cm

Therefore, the perimeter of the semi-circle is 180 cm.

Answer 2

✯✯ QUESTION ✯✯

The area of a semicircle is 1925 cm2. Calculate its perimeter (in cm).

A) 360 B) 80 C) 160 D) 180

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✰✰ ANSWER ✰✰

• Area of Semi Circle = 1925 cm²
• Perimeter of Semi Circle = ?

➮Firstly we will Find the Radius of Semi Circle ..

➥Using Formula : -

$\longmapsto\tt{\large{\boxed{\bold{\bold{\red{\sf{Area\:of\:Semicircle=\dfrac{\pi{{r}^{2}}}{2}}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{1925=\dfrac{22\times{{r}^{2}}}{7\times{2}}}$

$\longmapsto\tt{1925=\dfrac{22{r}^{2}}{14}}$

$\longmapsto\tt{1925\times{14}=22{r}^{2}}$

$\longmapsto\tt{26950=22{r}^{2}}$

$\longmapsto\tt{\cancel\dfrac{26950}{22}={r}^{2}}$

$\longmapsto\tt{\sqrt{1225}={r}^{2}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{r}\orange{=}\purple{35}}}$

☛So , The Radius of Semicircle is 35 cm ..

➥Now ,

➥Using Formula : -

$\longmapsto\tt{\large{\boxed{\bold{\bold{\blue{\sf{Perimeter\:of\:Semicircle=\pi{r+2r}}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{\dfrac{22}{7}\times{35}+2\times{35}}$

$\longmapsto\tt{22\times{5}+70}$

$\longmapsto\tt{110+70}$

$\longmapsto\tt\bold{180cm}$

☛So , The perimeter of semi circle is 180cm...

✔Therefore Option D) is Correct...