When the contents of a cylinder are poured into a second cylinder whose radius is 2 inches greater, the height reached in the second cylinder is one half of that reached in the first. Find to the nearest tenth of an inch the radii of the two cylinders.
2
r2h = (r + 2)2h
2r2h = (r2 + 4r + 4)h
2r2 = r2 + 4r + 4
r2 – 4r – 4 = 0
r2h = (r + 2)2h2
r2h = (r2 + 4r + 4)h2r2 = r2 + 4r + 4
r2 – 4r – 4 = 0
| r = | 4 ± √16 – 4 (-4) | = | 4 ± √32 | = | 4 ± 4√2 |
| 2 | 2 | 2 |
r = 2 ± 2√2
To make r positive, we choose +:
r = 2 + 2√2 ≈ 4.8 in (smaller)
and r + 2 ≈ 6.8 in (larger)
To make r positive, we choose +:
r = 2 + 2√2 ≈ 4.8 in (smaller)
and r + 2 ≈ 6.8 in (larger)