Question
Download Solution PDFIf the radius of a cylinder is doubled and the height is halved, then the volume change will be:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Original cylinder has radius R and height H.
New cylinder has radius 2R and height H/2.
Formula Used:
Volume of a cylinder (V) = π × radius2 × height = πR2H
Calculation:
Original volume (Voriginal) = πR2H
New volume (Vnew) = π × (2R)2 × (H/2)
Vnew = π × (4R2) × (H/2) = 2πR2H
Volume change = Vnew - Voriginal = 2πR2H - πR2H = πR2H
Percentage change in volume = [(Vnew - Voriginal) / Voriginal] × 100
Percentage change = (πR2H / πR2H) × 100 = 1 × 100 = 100%
The volume will increase by 100%.
Last updated on Jul 16, 2025
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