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Mathematics — CBSE Class 10 board question

Q1. [1]
If the volumes of two cubes are in the ratio $8:125$, then the ratio of their surface areas is:
  1. A $8:125$
  2. B $4:25$
  3. C $2:5$
  4. D $16:25$
Previously asked in CBSE board exam
2025 30/3/1 Q12
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer

Option B: 4 : 25

If volume ratio = 8 : 125, then side ratio = $\sqrt[3]{8} : \sqrt[3]{125}$ = 2 : 5. Surface area ratio = $2^2 : 5^2$ = 4 : 25.

Explanation

Key concept: Volume of cube $\propto a^3$ and surface area $\propto a^2$. Find the cube root of the volume ratio to get the side ratio, then square it for the surface area ratio. Don't confuse volume ratio directly with surface area ratio.

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