Question

The diagram shows a logo made from three circles.
Each circle has centre O.
Daisy says that exactly 1/3 of the logo is shaded.
Is Daisy correct?
You must show all your working.

Answer 1

Step-by-step explanation:

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

• The biggest one with its radius: 2+2+2= 8 cm
• The medium one with its radius: 2+2 = 4 cm
• The smallest one with its radius: 2 cm

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

$A = \pi \times {r}^{2}$

The area of the biggest circle is: π = 64π

The area of the medium circle is: π = 16π

The area of the smallest circle is: π = 4π

So the area of the shade part is:

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

= 64π - 4π

= 60π

So the percentage of the logo is shaded blue:

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

= 60π / 64π

= 0.9375

Answer 2

Answer:

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

The biggest one with its radius: 2+2+2= 8 cm

The medium one with its radius: 2+2 = 4 cm

The smallest one with its radius: 2 cm

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

A = \pi \times {r}^{2}A=π×r

2

The area of the biggest circle is: π = 64π

The area of the medium circle is: π = 16π

The area of the smallest circle is: π = 4π

So the area of the shade part is:

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

= 64π - 4π

= 60π

So the percentage of the logo is shaded blue:

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

= 60π / 64π

= 0.9375