The Square Footage Calculation of a Circular Retail Tower

What is the square footage of all floors in terms of π?

Given a retail tower that is circular with 20 floors and a circumference around the building of 200π, what is the total square footage of all floors in terms of π?

Answer:

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

The square footage of all floors in a circular retail tower with a circumference of 200π is 200,000π square units. This calculation involves finding the radius of a single floor and then using the area formula for a circle.

Explanation:

To begin, we need to determine the radius (r) of a single floor. The circumference (C) of a circle is given by the formula C = 2πr. In this case, the circumference is 200π. By substituting the values, we find that the radius is 100 feet.

Next, we calculate the area (A) of a single floor using the formula A = πr². Substituting the radius into the equation gives us A = π(100)² = 10,000π square feet for one floor.

Since the tower has 20 floors, the total area of all floors is determined by multiplying the area of one floor by the number of floors, which equals 20 times 10,000π = 200,000π square feet in total.