Consider five circles with radii of 1, 2, 4, 8, and 16 inches. Complete the chart. (Answers will be in terms of Pi). One has been completed for you.
|Radius|Circumference|Area|
|1|2pi in.|pi in.^2|
|2|
|4|
|8|
|16|
Help I have no idea what I'm supposed to do
c = 2πr
a = πr^2
so, plug in various values for r:
r c a
1 2π π
2 4π 4π
...
16 32π 256π
when 2r is substituted for r, you have new values for c and a:
2π(2r) and π(2r)^2
compare those to the original values using just r.
Part 2: Compare the areas and circumferences in the last problem.
What happens to the circumference and area of a circle when you double the radius?
No problem! To complete the chart, we need to calculate the circumference and area for the remaining circles.
The circumference of a circle can be found using the formula: C = 2πr, where r is the radius of the circle.
The area of a circle can be found using the formula: A = πr^2.
Let's go through each circle and calculate the circumference and area:
For a circle with radius 2 inches:
Circumference = 2πr = 2π(2) = 4π inches
Area = πr^2 = π(2^2) = 4π square inches
For a circle with radius 4 inches:
Circumference = 2πr = 2π(4) = 8π inches
Area = πr^2 = π(4^2) = 16π square inches
For a circle with radius 8 inches:
Circumference = 2πr = 2π(8) = 16π inches
Area = πr^2 = π(8^2) = 64π square inches
For a circle with radius 16 inches:
Circumference = 2πr = 2π(16) = 32π inches
Area = πr^2 = π(16^2) = 256π square inches
Now you can complete the chart!
|Radius|Circumference|Area|
|1|2π in.|π in.^2|
|2|4π in.|4π in.^2|
|4|8π in.|16π in.^2|
|8|16π in.|64π in.^2|
|16|32π in.|256π in.^2|