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Surface Areas and Volumes
NCERT Exemplar
CBSE
Grade 10
Question:
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14\text{ cm}$ and the total height of the vessel is $13\text{ cm}$. Find the inner surface area of the vessel.
Step-by-Step Solution
Key Concept: Radius $r = 7\text{ cm}$. Height of cylinder $h = 13 - 7 = 6\text{ cm}$. Inner SA $= \text{CSA of cylinder} + \text{CSA of hemisphere}$.
Radius $r = 7\text{ cm}$. Height of cylinder $h = 13 - 7 = 6\text{ cm}$. [0.5 Mark] CSA of cylinder $= 2\pi r h = 2 \times \dfrac{22}{7} \times 7 \times 6 = 264\text{ cm}^2$. [0.5 Mark] CSA of hemisphere $= 2\pi r^2 = 2 \times \dfrac{22}{7} \times 49 = 308\text{ cm}^2$. [0.5 Mark] Total inner SA $= 264 + 308 = 572\text{ cm}^2$. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Finding cylinder height $h = 6\text{ cm}$: 0.5 Mark CSA of cylinder $= 264\text{ cm}^2$: 0.5 Mark CSA of hemisphere $= 308\text{ cm}^2$: 0.5 Mark Total inner surface area $= 572\text{ cm}^2$: 0.5 Mark
Correct Answer:
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