Question

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

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

Answer 1

Answer:

area of semicircle = 1925 cm²

to find : perimeter P

area of semicircle = πr²/2

=> πr²/2 = 1925

=> r² = (1925 × 2) × 7/22

=> r² = 1225

=> 35 cm

Perimeter P = 2πr/2 + d

=> πr + 2r

=> 22/7 *35 + 2*35

=> 110 + 70

=> 180 cm

option D

Answer 2

$\huge\sf\pink{Answer}$

☞ Perimeter of the semi-circle is 180 cm

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Area of the semi-circle is 1925 cm²

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ Perimeter of the semi-circle

$\rule{110}1$

$\huge\sf\purple{Steps}$

Area of a semi-circle is given by,

$\underline{\boxed{\sf{Area\:of\: semicircle=\dfrac{\pi\:r^2}{2}}}}$

$\bullet\:\underline{\textsf{As Per the Question}}$

➝ $\sf{\dfrac{\pi\:r^2}{2}=1925}$

➝ $\sf{\pi\:r^2=1925\times\:2}$

➝ $\sf{\pi\:r^2=3850}$

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

➝ $\sf{r^2=3850\times\dfrac{7}{22}}$

➝ $\sf{r^2=1225}$

➝ $\sf{r=\sqrt{1225}}$

➝ $\red{\sf{r=35}}$

Perimeter of a semi-circle is given by,

$\underline{\boxed{\sf{Perimeter\:of\: semicircle=\pi\:r+d}}}$

Substituting the given values,

➢ $\sf \pi r+d$

➢ $\sf\dfrac{22}{7}\times 35 cm+70 cm$

➢ $\sf22 \times 5 cm+ 70 cm$

➢ $\sf\orange{Perimeter = 180\ cm}$

$\rule{170}3$