Question

32.Circumference of a semi-circle is 108 cm. Find the circumference of a circle whose radius is equal to the diameter of the semicircle. ​

Answer 1

The circumference of a circle whose radius is equal to the diameter of the semicircle is 432 cm.

Step-by-step explanation:

The circumference of a semi-circle = 108 cm

Let the radius of the semicircle be denoted as "r" cm.

We know

The circumference of a semicircle = πr

⇒ 108 = $\frac{22}{7}$ × r

⇒ r = $\frac{108 * 7}{22}$

⇒ r = 34.36 cm

Now, it is given that

[The radius of the circle] = [The diameter of the semicircle]

So, let the radius of the circle be denoted as "R" cm.

∴ R = 2 * r = 2 * 34.36 = 68.72 cm

Thus,

The circumference of the circle is given by,

= 2πR

= 2 × $\frac{22}{7}$ × 68.72

= 431.95

≈ 432 cm

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Answer 2

The circumference of circle is equal to 264 cm.

Step-by-step explanation:

Given,

The circumference of a semi-circle = 108 cm

To find, the circumference of a circle = ?

We know that,

The circumference of a semicircle = $\pi r+2r$

Given by question,

The radius of circle = The diameter of the semicircle

$\pi \dfrac{R}{2} +R=108$

⇒ $R(\dfrac{22}{7}+1) =108$

⇒ $R(\dfrac{22+14}{7}) =108$

⇒ $R(\dfrac{36}{7}) =108$

⇒ R = 42 cm

The circumference of circle = $2\pi R$

= $2\times \dfrac{22}{7} \times 42$

= 44 × 6 cm

= 264 cm

Thus, the circumference of circle is equal to 264 cm.