Question

The circumference of a circle is 30 cm.
(a)Calculate the radius of the circle.
(b)The length of the arc of the semi-circle is 15cm.
Calculate the area of the semi-circle.

Answer 1

Circumference = 30 cm

2πr = 30

r = 30/2π

r = 4.77 (approximately)

Now,

Length of the arc = 15 cm

Area of semicircle = ½lr = ½× 15 × 4.77 = 35.775 cm².

Answer 2

GIVEN : Circumference of circle = 30cm ; length of the arc of semi circle = 15cm

TO FIND :    Radius of circle ; area of semi circle

SOLUTION :

Circumference of Circle = 2× π× r

r here denotes Radius

   30 cm =  2 × 3.14 × r

   30 cm =  6.28 × r

   $\frac{30}{6.28}$   = r

   4.7 cm = r

Radius of the circle is 4.7 cm .

Area of semi circle = $\frac{1}{2}$ ×l ×r

Lenght of the arc is 15 cm and radius of the circle is 4.7cm .

So, area of semi circle = $\frac{1}{2}$ × 15 × 4.7

                                     = $\frac{1}{2}$ × 70.5

                                      = 35.25 cm²

Radius of the circle is 4.7 cm and area of the semi circle is 35.25 cm².