Either increasing the radius or the height of a cylinder by six inches will result in the same volume. The original height of the cylinder is two inches. What is the original radius?

Guest May 28, 2020

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*Either increasing the radius or the height of a cylinder by six inches will result in the same volume. The original height of the cylinder is two inches. What is the original radius?*

Volume of a Cylinder = π • r^{2} • h

If you increase the radius by 6 the new volume will be π • (r+6)^{2} • 2

If you increase the height by 6 the new volume will be π • r^{2} • (2+6)

Set the new volumes equal and solve for r

π • (r^{2} + 12r + 36) • 2 = π • r^{2} • 8

First, let's divide both sides by π (r^{2} + 12r + 36) • 2 = r^{2} • 8

Next, let's divide both sides by 2 r^{2} + 12r + 36 = r^{2} • 4

Subtract r^{2} from both sides 12r + 36 = 3r^{2}

Subtract (12r + 36) from both sides 0 = 3r^{2} – 12r – 36

Switch sides, just cuz I prefer the zero on the right 3r^{2} – 12r – 36 = 0

Factor the quadratic (3r + 6)(r – 6) = 0 This is the hardest step, IMHO.

Set each factor equal to zero 3r + 6 = 0

r = –2 Discard... can't have negative radius.

r – 6 = 0

**r = 6** The original radius was 6. .

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Guest May 29, 2020