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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10

Question:

The total surface area of a cube is $96\text{ cm}^2$. The volume of the cube is:
(a) $64\text{ cm}^3$
(b) $16\text{ cm}^3$
(c) $36\text{ cm}^3$
(d) $27\text{ cm}^3$

Step-by-Step Solution

Key Concept: $6 a^2 = 96 \Rightarrow a^2 = 16 \Rightarrow a = 4\text{ cm} \Rightarrow \text{Volume} = 4^3 = 64\text{ cm}^3$.
$a^2 = 16 \Rightarrow a = 4\text{ cm} \Rightarrow \text{Volume} = 64\text{ cm}^3$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Calculating volume $= 64\text{ cm}^3$: 1.0 Mark

Correct Answer: $64\text{ cm}^3$
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