Cylinder, Cone and Sphere — Mathematics STD 10 — Question
ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere2 Marks
Question
A cone and hemisphere have the same base and the same height. Find the ratio between their volumes.
✓
Answer
Let the radius of base be 'r' and the height be 'h'
Volume of cone, $V_c$
$=\frac{1}{3} \pi r^2 h$
Volume of hemisphere, $V_h$
$=\frac{2}{3} \pi r^2 h$
$\frac{V_c}{V_h}=\frac{\frac{1}{3} \pi r^2 r}{\frac{2}{3} \pi r^3} $
$ \Rightarrow \frac{V_c}{V_h}=\frac{1}{2}$
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