Question

The diagram shows a logo made from three circles

each circle has centre O


what percentage of the logo is shaded blue?

Answer 1

The percentage of the logo is shaded blue: 24%

Explanation:

From the given photo, we can see there are 3 circles.

• The biggest one with its radius: 5+2+3 = 10 cm
• The medium one with its radius: 5+2 = 7 cm
• The smallest one with its radius: 5 cm

After that, we find the area of each circle with the following formula:

A =π
`r^(2)`

• The area of the biggest circle is: π
  `10^(2)` = 100π
  `cm^(2)`
• The area of the medium circle is: π
  `7^(2)` = 49π
  `cm^(2)`
• The area of the smallest circle is: π
  `5^(2)` = 25π
  `cm^(2)`

So the area of the shade part is:

The area of the medium circle - The area of the smallest circle

= 49π
`cm^(2)` - 25π
`cm^(2)`

= 24π
`cm^(2)`

So the percentage of the logo is shaded blue:

= The area of the shaded blue / The area of the biggest circle

= 24π
`cm^(2)` / 100π
`cm^(2)`

= 0.24

= 24%