On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream for you.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding stimulus
Model Answer
(i) Diagonal of a cube = $\sqrt{3} \times \text{edge}$
$$= \sqrt{3} \times 6 = 6\sqrt{3} \text{ cm}$$
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(ii) Volume of a cube = $(\text{edge})^3$
$$= (7)^3 = 343 \text{ cm}^3$$
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(iii) Curved Surface Area of hemisphere = $2\pi r^2$
$$= 2 \times \frac{22}{7} \times 7 \times 7$$
$$= 2 \times 22 \times 7 = 308 \text{ cm}^2$$
The curved surface area of the hemisphere (ice-cream) is 308 cm².
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Source: Surface Areas and Volumes, NCERT Class 10 Mathematics
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Explanation
- (i) The space diagonal of a cube with edge $a$ is $a\sqrt{3}$. Students sometimes confuse face diagonal ($a\sqrt{2}$) with space diagonal — use $\sqrt{3}$ here.
- (ii) Volume of cube = side³. Straightforward substitution; unit must be cm³.
- (iii) CSA of hemisphere = $2\pi r^2$ (not $3\pi r^2$, which is total surface area). Being a 2-mark question, show the formula, substitution, and final answer clearly with units.