Question

teh face of a circular game token has an area of 10pi cm to the second power. what is the diameter of the coin token. round to the nearest hundredth of a centimeter

Answer 1

Area of a circle =
`πr²`

Given area =
`10π cm²`

`\bold\red{ ⇒} 10π = πr²`

`\bold\red{⇒ } 10 = r²`

`\bold\red{⇒ } r = √(10)`

Diameter = [tex]2r[/tex]

`\bold\red{⇒}2√(10) =\bold\pink{6.32 cm}`
`\bold\green{ [nearest \: hundredth]}`

Answer 2

6.32 cm

Explanation:

Area of a circle =
`\pi r^2` (where r is the radius)

Given area =
`10\pi` cm²

⇒
`10\pi=\pi r^2`

`\implies 10=r^2`

`\implies r=√(10)`

Diameter = 2r (where r is the radius)

`\implies d=2r=2√(10)=6.32` cm (nearest hundredth)