An engineer is designing a cylinder-shaped structure using the formula shown below. As shown, an approximation of 22/7
for pie is used in the formula.
v= 22/7r^2h
The engineer is considering using different values for , the radius in meters, and , the height in meters. Which pair of values makes , the volume in cubic meters, an irrational number?
A. r=3
and h=6.54
B. r=√11
and h=6.54
C. r=√11
and h = √9
D. r=3 and h=√15
An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite, non-repeating decimal representation.
To determine which pair of values makes the volume an irrational number, we need to check if the radicand (the number inside the square root) in the formula is an irrational number.
Let's calculate the possible pairs:
A. r=3 and h=6.54
Volume = (22/7)*(3^2)*(6.54) = 604.5714285714286
B. r=√11 and h=6.54
Volume = (22/7)*(√11^2)*(6.54) = (22/7)*(11)*(6.54) = 332.28571428571433
C. r=√11 and h = √9
Volume = (22/7)*(√11^2)*(√9) = (22/7)*(11)*(3) = 94
D. r=3 and h=√15
Volume = (22/7)*(3^2)*(√15) = (22/7)*(9)*(√15) = 93.24904133236172
Looking at the results, the only pair that results in an irrational number is option B: r=√11 and h=6.54.
Therefore, the correct answer is B. r=√11 and h=6.54.