Question

The diagram shows a logo made from three circles each circle has a centre 0 what percentage of the logo is shaded blue you must show all your working and your final answer must include the % sighs

Answer 1

Given that,

A logo made from three circles each circle has a centre O.

We need to calculate the area of small circle

Using formula of area

$A_{1}=\pi r^2$

Put the value into the formula

$A_{1}=\pi\times(5)^2$

$A_{1}=78.53\ m^2$

We need to calculate the area of middle circle

Using formula of area

$A_{2}=\pi r^2$

Put the value into the formula

$A_{2}=\pi\times(7)^2$

$A_{2}=153.93\ m^2$

We need to calculate the area of big circle

Using formula of area

$A_{3}=\pi r^2$

Put the value into the formula

$A_{3}=\pi\times(10)^2$

$A_{3}=314.1\ m^2$

The percentage of big circle is 100%.

We need to calculate the percentage of middle circle with small circle

Using formula of percentage

$percentage\ of\ middle\ with\ small\ circle = \dfrac{area\ of \ middle\ circle}{area\ of\ big\ circle}$

Put the value into the formula

$percentage\ of\ middle\ with\ small\ circle =\dfrac{153.93}{314.1}\times100$

$percentage\ of\ middle\ with\ small\ circle =49.0\%$

We need to calculate the percentage of small circle

Using formula of percentage

$percentage\ of\ small\ circle = \dfrac{area\ of \ small\ circle}{area\ of\ big\ circle}$

Put the value into the formula

$percentage\ of\ middle\ with\ small\ circle =\dfrac{78.53}{314.1}\times100$

$percentage\ of\ middle\ with\ small\ circle =25.0\%$

We need to calculate the percentage of shaded blue

Using formula of percentage

Percentage of shaded blue = percentage of medium circle - percentage of small circle

Put the value into the formula

$percentage\ of\ shaded\ blue=49-25$

$percentage\ of\ shaded\ blue=24\%$

Hence, The percentage of shaded blue is 24%.