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Home » The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.
The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.
Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20A | ICSE | Selina
The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.

The radius of a solid right cylinder (r) = 100 cm

let the height of a solid right circular cylinder (h) = 100 cm

The volume (original) of a solid right circular cylinder

    \[\begin{array}{*{35}{l}} =\text{ }\pi {{r}^{2}}h \\ =\text{ }\pi \text{ x }{{\left( 100 \right)}^{2}}~x\text{ }100 \\ =\text{ }10000\text{ }\pi \text{ }c{{m}^{3}} \\ \end{array}\]

Now, the new radius = r’ = 120 cm

New height = h’ = 80 cm

Therefore, the volume (new) of a solid right circular cylinder

    \[\begin{array}{*{35}{l}} =\text{ }\pi r{{}^{2}}h\text{ }=\text{ }\pi \text{ x }{{\left( 120 \right)}^{2}}~x\text{ }80 \\ =\text{ }1152000\text{ }\pi \text{ }c{{m}^{3}} \\ \end{array}\]

Thus, the increase in volume = New volume – Original volume

    \[\begin{array}{*{35}{l}} =\text{ }1152000\text{ }\pi \text{ }c{{m}^{3}}~-\text{ }1000000\text{ }\pi \text{ }c{{m}^{3~}} \\ =\text{ }152000\text{ }\pi \text{ }c{{m}^{3}} \\ \end{array}\]

Therefore, percentage change in volume = Increase in volume/Original volume x 100%

    \[\begin{array}{*{35}{l}} =\text{ }152000\text{ }\pi \text{ }c{{m}^{3}}/\text{ }1000000\text{ }\pi \text{ }c{{m}^{3}}~x\text{ }100% \\ =\text{ }15.2\text{ }% \\ \end{array}\]

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