Question

Which real world problem is most likely to involve irrational numbers?
A. Finding the diameter of a circle based on the radius
B. Finding the total cost of filling up a car's tank based on the price per gallon
C. Finding the side length of a square based on the area
D. Finding the width of a rectangle based on the area and the length

Answer 1

A. Finding the diameter of a circle based on the radius is most likely to involve irrational numbers. This is because the diameter \(d\) is calculated using the formula \(d = 2r\), where \(r\) is the radius. However, the circumference \(C\) of a circle is given by \(C = \pi d\), and since \(\pi\) is an irrational number, any calculations involving the circumference will also likely involve irrational numbers.

In the other options:
- B involves basic arithmetic and does not inherently involve irrational numbers.
- C (finding the side length of a square based on the area) can involve irrational numbers depending on the area (e.g., the side length of a square with area 2 is \(\sqrt{2}\)).
- D (finding the width of a rectangle based on the area and the length), could also involve irrational numbers, depending on the values involved.

However, option A is the most direct answer regarding the inherent use of an irrational number, \(\pi\), in calculations involving circles.