Sabrina is ordering a custom circular glass table for her dining room. The tables are ordered based on the area of the tabletop, and the diameter of every tabletop is a whole number. She wants a table with enough room for at least 6 people and wants each person to have at least 5 feet of table edge space, so that it is not too crowded.
The minimum tabletop diameter Sabrina should order is
feet.
The minimum tabletop area of the table Sabrina should order is
square feet.
The minimum tabletop diameter Sabrina should order is 10 feet.
To calculate the minimum tabletop area, we first need to find the circumference of the table to determine the amount of table edge space each person will have. The circumference of a circle is calculated by the formula C = πd, where d is the diameter.
Given that each person should have at least 5 feet of table edge space, we can calculate the circumference needed:
C = 6 people * 5 feet = 30 feet
Since the diameter is a whole number, we know that the minimum diameter Sabrina should order is 10 feet. Therefore, the minimum tabletop area is:
A = π(10/2)^2
A = π(5)^2
A = 25π square feet
A ≈ 78.54 square feet
So, the minimum tabletop area of the table Sabrina should order is approximately 78.54 square feet.