What is the circumference and area of a circle with a diameter of 13 centimeters?

2 Answers
Oct 17, 2015

Formula for circumference of a circle:

#C = 2.pi.r #

where,

r is the radius of the circle.

# r = (diameter) / 2#
# r = 13 / 2 #
# r = 6.5# centimeters.

# C = 2. 3142.6.5#
# C = 40.846 # centimeters

Formula for Area of a Circle:

# A = pi.r^2 #
# A = 3.142 . (6.5)^2 #
# A = 132.7495 # Sq. centimeters

Oct 17, 2015

Answer:

The circumference is #2pi r = 2pi*13/2 = 13pi ~~ 40.84cm#
The area is #pi r^2 = pi (13/2)^2 = (169pi)/4 ~~ 132.73cm^2#

Explanation:

#pi# is defined as the ratio between the circumference of a circle and its diameter. #pi# is an irrational number, so it cannot be represented as a fraction or a repeating decimal.

Popular rational approximations for #pi# are #22/7 = 3.dot(1)4285dot(7)# and the less well known but really good #355/113 ~~ 3.1415929#.

So the circumference of our circle will be #pi * 13cm = 13pi cm ~~ 13*355/113 ~~ 40.84cm#

The formula more commonly used is #2pir#, where #r# is the radius of the circle.

The formula for the area of a circle is #pir^2#, where #r# is the radius.

In our case we have:

#"area" = pi r^2 = pi (13/2)^2 = pi (13^2/2^2) = pi (169/4) ~~ (355*169)/(113*4) = 59995 / 452 ~~ 132.73cm^2#

Why is the area #pi r^2#?

You can divide a circle of radius #r# into a number of segments and rearrange them head to tail to form a sort of bumpy parallelogram with long side roughly #pi r# and height #r#, therefore area #pi r * r = pi r^2#.

This work better the more segments you have, but here's an illustration for just #8# segments...

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