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Surface Areas and Volumes
RD Sharma
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 total height of vessel is $13\text{ cm}$. The inner surface area of the vessel is:
(a) $572\text{ cm}^2$
(b) $440\text{ cm}^2$
(c) $264\text{ cm}^2$
(d) $616\text{ cm}^2$
(a) $572\text{ cm}^2$
(b) $440\text{ cm}^2$
(c) $264\text{ cm}^2$
(d) $616\text{ cm}^2$
Step-by-Step Solution
Key Concept: Radius $r = 7\text{ cm}$. Height of cylinder $h = 13 - 7 = 6\text{ cm}$. Inner Surface Area $= 2 \pi r h + 2 \pi r^2 = 2 \pi r (h + r) = 2 \times \dfrac{22}{7} \times 7 \times (6 + 7) = 44 \times 13 = 572\text{ cm}^2$.
$r = 7\text{ cm}, h = 6\text{ cm}$. [0.5 Mark]
$\text{Area} = 2 \pi r(h + r) = 2 \times \dfrac{22}{7} \times 7 \times 13 = 44 \times 13 = 572\text{ cm}^2$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Finding cylinder height $h = 6\text{ cm}$: 0.5 Mark
Evaluating total inner surface area $= 572\text{ cm}^2$: 0.5 Mark
$\text{Area} = 2 \pi r(h + r) = 2 \times \dfrac{22}{7} \times 7 \times 13 = 44 \times 13 = 572\text{ cm}^2$. [0.5 Mark]
---
🎯 Official CBSE Marking Scheme:
Finding cylinder height $h = 6\text{ cm}$: 0.5 Mark
Evaluating total inner surface area $= 572\text{ cm}^2$: 0.5 Mark
Correct Answer: $572\text{ cm}^2$
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