Question

The Perimeter of a semi-circle is 32.4 cm. Calculate i) radius of the semicircle
ii) the area of the semicircle.

Answer 1

Given :

Perimeter of a semi- circle is 32.4 cm

To Find :

1. Radius of the semi- circle
2. Area of the semi - circle

Solution :

Let the radius of the semi- circle be ' r '

1) We have to find the radius of the semi- circle

We know that perimeter of a semi- circle is πr+2r

Thus ,

Perimeter = 32.4 cm

$\sf\implies\pi\:r+2r=32.4\:cm$

$\sf\implies\:(\pi+2)r=32.4\:cm$

$\sf\implies(\dfrac{22}{7}+2)r=32.4\:cm$

$\sf\implies(\dfrac{36r}{7})=32.4\:cm$

$\sf\implies\:r=\dfrac{32.4\times7}{36}$

$\sf\implies\:r=\dfrac{226.8}{36}$

$\sf\implies\:r=6.3\:cm$

Hence , Radius of the semi- circle is 6.3 cm.

2) We have to find the area of the semi- circle

We know that the area of the semi- circle is πr²/2

Thus ,

${\sf\:Area}=\sf\dfrac{\pi\times\:r^{2}}{2}$

$\sf=\dfrac{22\times(6.3)^{2}}{7\times2}$

$\sf=\dfrac{22\times39.69}{14}$

$\sf=\dfrac{873.18}{14}$

$\sf=62.37\:cm^{2}$

Hence , Area of the semi - circle is 62.37 cm².

Answer 2

• As per the data given in the question, we have to find the value of the expression.    

           Given data:- Parameter of the semicircle is $32.4.$  

           To find:- Radius and are of the semicircle.

            Solution:-

• We know that the perimeter of a semicircle is $\pi r+2r.$

                   $\begin{array}{l}r+2 r=32.4 \mathrm{~cm} \\(\pi+2) r=32.4 \mathrm{cr} \\\left.(\frac{22}{7}+2\right) r=32.4 c \\\left.(\frac{36 r}{7}\right)=32.4 \mathrm{~cm} \\r=\frac{32.4 \times 7}{36}\end{array}\\\begin{array}{l}r=\frac{220.8}{36} \\r=6.3 \mathrm{~cm}\end{array}$

        Hence radius of a semicircle is $6.3cm.$

• We know that the area of the semi-circle is $\frac{\pi r^{2} }{2} .$  

                  $\frac{\pi (6.3^{2}) }{2} \\=62.34cm^{2} .$

    Hence the area of semi-circle is $62.34cm^{2} .$