An engineer is designing a cylinder-shaped structure using the formula shown below. As shown, an approximation of 22/7 is used for π the formula.
V = 22/7 r^2 h
The engineer is considering different values for r, the radius in meters, and h, the height in meters. Which pair of values make V the volume in cubic meters, an irrational numbers?
a. r = √5 and h = 3.17
b. r = √5 and h = √16
c. r = 2 and h = √13
d. r = 2 and h = 3.17
To determine if the volume is an irrational number, we need to check if the values of r and h result in an irrational value for V.
Let's calculate the volume for each pair of values:
a. r = √5 and h = 3.17
V = (22/7)(√5)^2(3.17)
V = (22/7)(5)(3.17)
V = (22/7)(15.85)
V = 48.5714...
This is a rational number, not an irrational number.
b. r = √5 and h = √16
V = (22/7)(√5)^2(√16)
V = (22/7)(5)(4)
V = (22/7)(20)
V = 62.8571...
This is a rational number, not an irrational number.
c. r = 2 and h = √13
V = (22/7)(2)^2(√13)
V = (22/7)(4)(√13)
V = (22/7)(4√13)
V = 44√13
This is an irrational number.
d. r = 2 and h = 3.17
V = (22/7)(2)^2(3.17)
V = (22/7)(4)(3.17)
V = (22/7)(12.68)
V = 40
This is a rational number, not an irrational number.
Therefore, the pair of values that make V an irrational number is c. r = 2 and h = √13.