Two circles have the same radius. Is the combined area of the two circles the same as the area of a circle with twice the radius? Explain.
THANK YOU!
no!
Two circles of radius r
= 2(π)(r^2)
= 2π r^2
one circle of radius 2r
= π(2r)^2
= 4π r^2
use an example, eg. r = 3
two circles with r = 3
= 2π(3^2) = 18π
one circle with radius 6
= π(6^2)
= 36π
notice the singe large circle is twice the area of the two smaller ones
I dont think that answers the question it is to hard to understand
some things are harder for others
To determine if the combined area of two circles with the same radius is the same as the area of a circle with twice the radius, we need to calculate the areas of both scenarios.
Let's define the radius of the circles as 'r'. The area of a circle is given by the formula A = πr^2.
For the first scenario, where two circles have the same radius 'r', the combined area would be the sum of the areas of both circles. So, the combined area is:
A1 = πr^2 + πr^2
= 2πr^2
Now, let's consider the second scenario where we have a circle with twice the radius, which we'll denote as '2r'. The area of this circle is given by:
A2 = π(2r)^2
= π(4r^2)
= 4πr^2
Comparing A1 and A2, we have 2πr^2 for the combined area of two circles with radius 'r', and 4πr^2 for the area of a circle with radius '2r'.
Since 4πr^2 is twice the value of 2πr^2, it shows that the combined area of two circles with the same radius is NOT the same as the area of a circle with twice the radius. The area of a circle with twice the radius is greater.
In conclusion, the combined area of two circles with the same radius is not equal to the area of a circle with twice the radius.