A clock tower has a circular clock face with an area of #144pi# square feet. What is the diameter of the clock face?

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Answer 1 · 2017-03-05T05:02:50

The diameter of the clock face is #24# feet.

The formula for the area of a circle is:

#A=pir^2#

Since we know the area, we can calculate the radius and double that to determine the diameter of the clock face.

#144pi=pir^2#

Cancel the like terms on each side.

#144cancelpi=cancelpir^2#

#144=r^2#

Factorise #144# to determine the radius.

#2*2*2*2*3*3=r^2#

#(2*2*3)(2*2*3)=r^2#

#(2*2*3)^2=r^2#

#2*2*3=r#

#r=12#

Hence the diameter (#2r#) will be:

#D=2xx12=24#