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Surface Areas and Volumes
NCERT Exemplar
CBSE
Grade 10
Question:
If the radius of the base of a right circular cylinder is halved, keeping the height same, the ratio of the volume of the reduced cylinder to that of the original cylinder is: (a) $2 : 1$ (b) $1 : 2$ (c) $1 : 4$ (d) $4 : 1$
Step-by-Step Solution
Key Concept: Original volume $V_1 = \pi r^2 h$. New volume $V_2 = \pi (r/2)^2 h = \dfrac{\pi r^2 h}{4} = \dfrac{V_1}{4}$.
Ratio $V_2 / V_1 = \dfrac{\pi (r/2)^2 h}{\pi r^2 h} = \dfrac{1}{4}$. Ratio is $1 : 4$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Evaluating volume ratio $= 1:4$: 1.0 Mark
Correct Answer:$1 : 4$
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