An engineer is designing a cylinder-shaped structure using the formula shown below. As shown, an approximation of 22/7 for pi for is used in the formula.
The engineer is considering using different values for r , the radius in meters, and h , the height in meters. Which pair of values makes V , the volume in cubic meters, an irrational number?
r=3 and h=6.54
r=\sqrt(11) and h=6.54
r=\sqrt(11) and h=\sqrt(9)
r=3 and h=\sqrt(15)
To determine if the volume is an irrational number, we need to calculate the value of V in each case using the given formula:
V = π * r^2 * h
For r=3 and h=6.54:
V = (22/7) * 3^2 * 6.54 = (22/7) * 9 * 6.54 = 558.8571428571429
The volume in this case is a rational number.
For r=√11 and h=6.54:
V = (22/7) * (√11)^2 * 6.54 = (22/7) * 11 * 6.54 = 252.57142857142861
The volume in this case is a rational number.
For r=√11 and h=√9:
V = (22/7) * (√11)^2 * (√9) = (22/7) * 11 * 3 = 93.42857142857143
The volume in this case is a rational number.
For r=3 and h=√15:
V = (22/7) * 3^2 * (√15) = (22/7) * 9 * (√15) = 148.28571428571428
The volume in this case is a rational number.
Therefore, none of the given pairs of values for r and h make the volume V an irrational number.