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19 December, 08:21

A retail tower is circular with 20 floors. The circumference around the building is 200π. What is the square footage of all floors in terms of π?

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  1. 19 December, 10:11
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    The area of all floors=200,000π square foot

    Explanation:

    Step 1: Determine the circumference of one floor

    Since the retail tower is circular in shape with a circumference of 200π, it means one floor has a perimeter of 200π.

    The formula for the circumference of a circle is;

    C=2πr

    where;

    C=circumference of the circle

    π=pi

    r=radius of the circular tower

    In our case;

    C=200π

    r=unknown

    replacing;

    200π=2πr

    r=200π/2π

    r=100 feet

    Step 2: Determine the Area of one circular floor

    The area of a circle is given as;

    A=πr^2

    where;

    r=100 feet

    A=unknown

    replacing;

    A=π*100^2

    A=10,000π square foot

    The area of one floor=10,000π square foot

    Area of all floors=area of one floor*number of floors

    where;

    area of one floor=10,000π square foot

    number of floors=20

    replacing;

    Area of all floors=20*10,000=200,000π square foot
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