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Cylinder, Cone and Sphere — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere4 Marks
Question
The radius of a solid right circular cylinder increases by $20\%$ and its height decreases by $20\%$. Find the percentage change in its volume.
✓

Answer

Let the radius of a solid right circular cylinder be r = 100 cm
And let the height of a solid right circular cylinder be $h = 100 cm$
$\therefore $ Volume (original) of a solid right circular cylinder
$=\pi r ^2 h$
$=\pi \times(100)^2 \times 100$
$=1000000 \pi cm ^3$
New radius $= r' = 120 cm$
New height $= h' = 80 cm$
$\therefore $ Volume (New) of a solid right circular cylinder $= \pi '^2 h'$
$= \pi \times (120)^2 \times 80$
$= 1152000 \pi cm^3$
$\therefore $ Increase in volume = New Volume - Original Volume
$= 1152000 \pi cm^3 - 1000000 \pi cm^3$
$= 152000 \pi cm^3$​​​​​​​
Thus , Percentage change in volume =$\frac{\text { Increase in volume }}{\text { Original Volume }} \times 100 \%$
$=\frac{152000 \pi cm ^3}{1000000 \pi cm ^3} \times 100 \%$
$=15.2 \%$

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