Final answer:
Formulas for the area of a circle and the volume and surface area of a sphere contain the irrational number π (pi). The perimeter of a square formula does not contain an irrational number.
Step-by-step explanation:
The question asks which formulas containing an irrational number. Looking at the formulas provided such as the area of a circle (A = πr²) and the volume of a sphere (V = 4/3 πr³), we can identify the presence of π (pi) which is an irrational number.
Therefore, the formula for the area of a circle and the volume of a sphere both contain an irrational number due to π. The perimeter of a square (P = 4s) does not include π and therefore does not contain an irrational number. The formula for the surface area of a sphere mentioned in the question seems to have a typo as the correct formula is SA = 4πr², which also contains the irrational number π.
The formulas that contain irrational numbers are:
Volume of a sphere: V = (4/3)πr³
Surface area of a sphere: SA = 4πr²
An irrational number is a number that cannot be expressed as a fraction or as a terminating or repeating decimal. The values of π (pi) and r in these formulas are irrational numbers. Pi is approximately equal to 3.1415927, and r represents the radius of the sphere, which can take any positive real value.