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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10
Question:
A cylindrical vessel of radius $4\text{ cm}$ contains water. A solid sphere of radius $3\text{ cm}$ is lowered into the water until it is completely immersed. The rise in water level in the vessel is: (a) $2.25\text{ cm}$ (b) $4.5\text{ cm}$ (c) $3.0\text{ cm}$ (d) $1.5\text{ cm}$
Step-by-Step Solution
Key Concept: $\pi (4)^2 h = \dfrac{4}{3} \pi (3)^3 \Rightarrow 16 h = 36 \Rightarrow h = 2.25\text{ cm}$.
$16 h = 36 \Rightarrow h = 2.25\text{ cm}$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Calculating water level rise $= 2.25\text{ cm}$: 1.0 Mark
Correct Answer:$2.25\text{ cm}$
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