The area of the bigger circle exceeds the combined area of the two smaller circles by 4Ï€ square meters.
Practice makes perfect
To find out by how many square meters the area of the bigger circle exceeds the combined area of the two smaller circles, we have to calculate the area of each circle. Let's start by recalling the formula for the area of a circle.
A=Ï€ r^2
In this formula r is the radius of the circle. First, we will calculate the area of the circle 6 meters in diameter. Note that we are given the diameter, not the radius. However, the radius is always half the diameter. Therefore, the radius of the first circle is equal to 3 meters.
The area A_1 of the first circle is equal to 9Ï€ square meters. Let's repeat the same process for the other two circles.
Diameter
Radius
Area
6 m
3 m
A_1=9Ï€ m^2
4 m
2 m
A_2=4Ï€ m^2
2 m
1 m
A_3=Ï€ m^2
Looking at the table, we can calculate the combined area of the two smaller circles.
A_2+A_3=4Ï€ +Ï€ =5Ï€
Finally, we will subtract the combined area of the two smaller circles from the area of the bigger circle.
A_1-(A_2+A_3)=9Ï€ -5Ï€ =4Ï€
The area of the bigger circle exceeds the combined area of the two smaller circles by 4Ï€ square meters.
