If the radius of a cylinder is doubled and the height is halved, then the volume change will be:

Given:

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 (V_original) = πR²H

New volume (V_new) = π × (2R)² × (H/2)

V_new = π × (4R²) × (H/2) = 2πR²H

Volume change = V_new - V_original = 2πR²H - πR²H = πR²H

Percentage change in volume = [(V_new - V_original) / V_original] × 100

Percentage change = (πR²H / πR²H) × 100 = 1 × 100 = 100%

The volume will increase by 100%.