The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?
A. X²/2π
B. X/2√π
C. √2X/π
D.π/√2X
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Given : Radius of cylinder = r
Side length of square base = x
Height of rectangular box = height of cylinder
Volume of a cylinder = 1/4 of the volume of a rectangular box
πr²h = ¼ × x × x × h
πr²h = ¼ × x² × h
πr² = ¼ × x × x
r² = x²/4π
r = ½ x √1/π
r = x/2√π
Option (B) x/2√π is correct.
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Answer:
Step-by-step explanation:
πr²h = ¼ × x × x × h
πr²h = ¼ × x² × h
πr² = ¼ × x × x
r² = x²/4π
r = ½ x √1/π
r = x/2√π
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