Find the ratio of the volume of a sphere to the volume of a cylinder having same radius and height equal to the diameter of the sphere.
Step-by-Step Solution
Key Concept: Sphere Vol $= \dfrac{4}{3} \pi r^3$. Cylinder Vol $= \pi r^2(2r) = 2 \pi r^3$. Ratio $= \dfrac{4/3}{2} = \dfrac{2}{3} \Rightarrow 2 : 3$.
$\text{Sphere Vol} = \dfrac{4}{3}\pi r^3$, $\text{Cylinder Vol} = 2\pi r^3$. [1.0 Mark]
Ratio $= \dfrac{4/3}{2} = 2 : 3$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Writing volume formulas with $h = 2r$: 1.0 Mark
Evaluating ratio $= 2 : 3$: 1.0 Mark
Correct Answer: