Question

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?

Answer 1

The square footage of all floors in a circular retail tower with a circumference of 200π is 200000π square units. This is calculated by first determining the radius from the circumference and then using the area formula for a circle.

Step-by-step explanation:

To calculate the square footage of all floors of a circular retail tower with a circumference of 200π, we start by finding the radius of a single floor. We know that the circumference (C) of a circle is given by the formula C = 2πr, where r is the radius. In this case, C = 200π. By doing the math, we can deduce that r = 100.

Then, to find the area (A) of a single floor, we use the area formula of a circle A = πr². Substituting the value of r into this equation gives us A = π(100)² = π10000π square units for one floor. Since the tower has 20 floors, the total area will be 20 times the area of one floor, which equals 20 * π10000π = 200000π square units.

Answer 2

The area of all floors=200,000π square foot

Step-by-step 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