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?
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 • r2 • 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 • r2 • (2+6)
Set the new volumes equal and solve for r
π • (r2 + 12r + 36) • 2 = π • r2 • 8
First, let's divide both sides by π (r2 + 12r + 36) • 2 = r2 • 8
Next, let's divide both sides by 2 r2 + 12r + 36 = r2 • 4
Subtract r2 from both sides 12r + 36 = 3r2
Subtract (12r + 36) from both sides 0 = 3r2 – 12r – 36
Switch sides, just cuz I prefer the zero on the right 3r2 – 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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