Answers:
1. Circumference is roughly 18.8 cm
2. Circumference is roughly 12.6 ft
3. Circumference is roughly 213.6 mm
6. Circumference is roughly 31.4 miles
7. Circumference is roughly 44.0 inches
10. Circumference is roughly 50.3 cm
Work Shown
Problem 1)
The formula used through all of these problems is going to be C = 2*pi*r where C is the circumference, pi = 3.1415... (goes on forever without a known pattern), and r is the radius
In this case, r = 3, so,
C = 2*pi*r
C = 2*pi*3
C = 2*3*pi
C = 6*pi
C = 18.8495559215388 <-- using a calculator here
C = 18.8
Problem 2)
Follow the same basic steps as problem 1
This time r = 2
C = 2*pi*r
C = 2*pi*2
C = 2*2*pi
C = 4*pi
C = 12.5663706143591 <-- using a calculator here
C = 12.6
Problem 3)
Follow the same basic steps as before. Now r = 34
C = 2*pi*r
C = 2*pi*34
C = 2*34*pi
C = 68*pi
C = 213.628300444106 <-- using a calculator here
C = 213.6
Problem 6)
Follow the same basic steps as before. Now r = 5
C = 2*pi*r
C = 2*pi*5
C = 10*pi
C = 31.415926535898 <-- using a calculator here
C = 31.4
Problem 7)
The side length of the square is 14 inches. The diameter of the circle is 14 inches because the circle is perfectly inside the square. The radius of the circle is r = d/2 = 14/2 = 7 inches.
So r = 7 will be plugged into the circumference formula
C = 2*pi*r
C = 2*pi*7
C = 2*7*pi
C = 14*pi
C = 43.9822971502571 <-- using a calculator here
C = 44.0
Problem 10)
This one is probably the most complicated of the whole batch. But it's not that bad. The first step we need to do is find the hypotenuse of the right triangle
Use the pythagorean theorem
a^2 + b^2 = c^2
(8*sqrt(3))^2 + (8)^2 = c^2
64*3 + 64 = c^2
192 + 64 = c^2
256 = c^2
c^2 = 256
c = sqrt(256)
c = 16
The diameter of the circle is equal to the hypotenuse.
The diameter of the circle is 16 cm
The radius of the circle is r = d/2 = 16/2 = 8 cm
Plug r = 8 into the circumference formula
C = 2*pi*r
C = 2*pi*8
C = 2*8*pi
C = 16*pi
C = 50.2654824574367 <-- using a calculator here
C = 50.3
