Question

The area of a semi-circle is 693 sq.cm. Find it's radius and perimeter​

Answer 1

Area of semi-circle = ½(area of circle)

Area of semi-circle = (∏r2) /2

⇒ 693 = (22/7) × r²/2

⇒ r² = (693 × 7 × 2) /22

⇒ r = 21

∴ Radius of semi-circle = 21 cm

The perimeter of a semicircle of radius 21 cm

= Arc length of semicircle + Diameter

= Diameter = 2 × 21 = 42 cm

= Arc length of Semi circle

= π R

= (22/7) × 21

= 22 * 3

= 66 cm

The perimeter of a semicircle of radius 21 cm = 42 + 66  = 108 cm.

Answer 2

• As per the data given in the question, we have to find the value of the expression.    Given data:- Area of the semicircle is $693 \ sq.cm.$

           To find:- Radius and parameter of the semicircle.

            Solution:-

• A semicircle is half of a circle.

                  $\begin{array}{l}\because \text { Area of semi-circle }=1 / 2(\text { area of circle }) \\\text { Area of semi-circle }=\left(\Pi r^{2}\right) / 2 \\\Rightarrow 693=(22 / 7) \times r^{2} / 2 \\\Rightarrow r^{2}=(693 \times 7 \times 2) / 22 \\\Rightarrow r=21 \\\therefore \text { Radius of semi-circle }=21 \mathrm{~cm}\end{array}$

              $\begin{array}{l}=\text { Arc length of semicircle + Diameter } \\=\text { Diameter }=2 \times 21=42 \mathrm{~cm} \\=\text { Arc length of Semi circle } \\=\pi R \\=(22 / 7) \times 21 \\=22 * 3 \\=66 \mathrm{~cm}.\end{array}$

   The perimeter of a semicircle of radius$=42+66=108 \mathrm{~cm}.$.