an engineer is designing a cylinder-shaped structure using the formula shown below. as shown, an approximation of 227 is used for π the formula. v=227r2h 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? (1 point) responses r=2 and h=3.17 r=2 and h=3.17 r=5–√ and h=16−−√ r=5–√ and h=16−−√ r=5–√ and h=3.17 r=5–√ and h=3.17 r=2 and h=13−−√ r=2 and h=13−−√

Question

an engineer is designing a cylinder-shaped structure using the formula shown below. as shown, an approximation of 227 is used for π the formula. v=227r2h 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? (1 point) responses r=2 and h=3.17 r=2 and h=3.17 r=5–√ and h=16−−√ r=5–√ and h=16−−√ r=5–√ and h=3.17 r=5–√ and h=3.17 r=2 and h=13−−√ r=2 and h=13−−√

Answer 1

The pair of values that make the volume an irrational number is r=5–√ and h=16–√.

Here's the calculation:

V = 227r^2h
V = 227(5-√)^2(16-√)
V = 227(25 - 10√ + (√2)^2)(16 - √4)
V = 227(25 - 10√ + 2)(16 - 2)
V = 227(25 - 10√ + 2)(14)
V = 227(350 - 140√ + 50 - 20√)
V = 227(400 - 160√ -140√)
V = 227(400 - 300√)
V = 227(400) - 68100√
V = 90800 - 68100√

Since √ is irrational, the volume V with r=5–√ and h=16–√ is also irrational.