Question

Consider the stage of the theatre which is a semi-circle. The diameter of the stage is 30m.

Calculate the area the actors have available to perform their art.

Answer 1

The area available to perform is 353.43 square meters

Explanation:

Given:

The diameter of the stage = 30m

The radius of the stage is half of its diameter.

So,

`\sf Radius = (30)/(2) = 15m.`

We have

`\textsf{ The area of a semi-circle }\sf = (1)/(2)\pi * r^2`

where

• π is approximately equal to
• r is the radius of the semi-circle.

Substituting value

`\sf \sf \textsf{ The area of the stage } = (1)/(2)* \pi * 15^2`

`\sf \textsf{ The area of the stage } = (1)/(2)* 3.141592654 * 15^2`

`\sf \textsf{ The area of the stage = 353.43$\sf m^2 $ in 2 d.p}`

Therefore, the actors have approximately 353.43 square meters of area available to perform their art.