Mathematics

The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.

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Let the radius of a solid right cylinder be r cm and height be h cm.

∴ Volume of cylinder = πr²h

New radius (r') = r + $\dfrac{20}{100} \times r = \dfrac{120r}{100}$ = 1.2r.

New height (h') = h - $\dfrac{20}{100} \times h = \dfrac{80h}{100}$ = 0.8h.

⇒ New volume of the solid right circular cylinder = πr'²h'

= π x (1.2r)² x 0.8h

= 1.152 πr²h.

Increase in volume = New volume - Original volume

= 1.152 πr²h - πr²h

= 0.152 πr²h.

By formula,

Percentage change in volume = $\dfrac{\text{Increase in volume}}{\text{Original volume}}$ x 100%

= $\dfrac{0.152πr^2h}{πr^2h}$ x 100%

= 15.2 %.

Hence, percentage change in volume = 15.2 %.

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