The length of radius of a right circular cylinder is decrcased by 50% and height is
increased by 50%, let us write how much percent of the volume will be changed.
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Answer:
If the radius of a cylinder is decreased by 50% and the height is increased by 50%, then what is the change in volume?
Let's call the initial volume of the cylinder “V1” and the “modified volume” (with the decrease in radius and increase in height) “V2".
The volume of a cylinder (V) is the area of its base (B) multiplied by its height (H).
V = B * H
The area of the base (“radius” = "R") is: π * R²
Therefore: V1 = π * R² * H
And if you decrease the radius by 50% and increase the height in 50%, you have:
V2 = π * (R/2)² * 1,5H = π * R² / 4 * 1,5 * H
Thus you have:
V1 = π * R² * H
V2 = π * R² * H / 4 * 1,5
V2 = V1 / 4 * 1,5
V2 = V1 * 0,375
Conclusion: The change in volume is a decrease of 62,5%
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