Final answer:
The formulas that contain both a rational and an irrational number are the volume of a sphere (V = 4/3 (πr³)), the surface area of a sphere (A = 4 (πr²)), and the area of a circle (A = πr²). Therefore, the answer is option A: Volume of Sphere, Surface Area of Sphere, Area of Circle.
Step-by-step explanation:
The student is asking about formulas involving both rational and irrational numbers within geometric contexts. Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, whereas irrational numbers cannot be expressed as a simple fraction and they have non-repeating, non-terminating decimal expansions.
The formula for the volume of a sphere is given by V = 4/3 (πr³), where π (pi) is an irrational number and 4/3 is a rational number. Similarly, the formula for the surface area of a sphere is A = 4 (πr²), which also contains both types of numbers. The formula for the area of a circle is A = πr², again containing both rational and irrational numbers, as the value for π and the square of the radius which is rational.
Therefore, the correct answer to the student's question is option A: Volume of Sphere, Surface Area of Sphere, Area of Circle. Each of these contains both a rational number and an irrational number, given that the sphere and circle geometries involve π, an irrational number, and the coefficients in the formulas are rational numbers.