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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10
Question:
A decorative block is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge $5\text{ cm}$, and the hemisphere fixed on the top has a diameter of $4.2\text{ cm}$. Find the total surface area of the block.
Step-by-Step Solution
Key Concept: Cube Area $= 6(25) = 150\text{ cm}^2$. Hemisphere $r = 2.1\text{ cm}$. Base area $= \dfrac{22}{7} \times 4.41 = 13.86\text{ cm}^2$. CSA hemisphere $= 2(13.86) = 27.72\text{ cm}^2$. Total Area $= 150 - 13.86 + 27.72 = 163.86\text{ cm}^2$.
Cube Area $= 6 \times 25 = 150\text{ cm}^2$. [1.0 Mark] Base circle area $= 13.86\text{ cm}^2$, Hemisphere CSA $= 27.72\text{ cm}^2$. [1.0 Mark] Total Area $= 150 - 13.86 + 27.72 = 163.86\text{ cm}^2$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Calculating cube surface area $= 150\text{ cm}^2$: 1.0 Mark Calculating hemisphere CSA & base area: 1.0 Mark Evaluating total block surface area $= 163.86\text{ cm}^2$: 1.0 Mark
Correct Answer:
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