Question

Here is a semicircle of diameter d.

the perimeter of the shape is 51.42cm
calculate the value of the diameter d

Answer 1

a) D
`(\pi d)/(2)+d`

b) 20 cm

Explanation:

a) circumference of circle =
`\pi d`

Therefore, perimeter of shape =
`(\pi d)/(2)+d`

b) Given:

• perimeter = 51.42 cm
• 
  `\pi` = 3.142

`\implies 51.42 =(3.142d)/(2)+d`

`\implies 51.42 =(3.142d)/(2)+(2d)/(2)`

`\implies 51.42 =(3.142d+2d)/(2)`

`\implies 51.42* 2 =3.142d+2d`

`\implies 102.84 =5.142d`

`\implies d=(102.84)/(5.142)`

`\implies d=20`