Question

If the perimeter of a semi circle is 216 cm, what is its diameter?

• A.
  84 cm
• B.
  82 cm
• C.
  42 cm
• D.
  80 cm

Answer 1

The correct option is A

84 cm
Given perimeter of a semicircle = 216 cm
Let $r$ be the radius of the semicircle.

Perimeter of semicircle = $2r$ (Straight line diameter) + $\pi r$ (Curved surface)

$\Rightarrow \pi r+2r=216$

$\Rightarrow r(\pi +2)=216$

$\Rightarrow r(\frac{22}{7}+2)=216$

$\Rightarrow r\left(\frac{22+14}{7}\right)=216$

$\Rightarrow r\times \frac{36}{7}=216\Rightarrow r=42$ cm

$\Rightarrow Diameter=2r=84$ cm