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The total surface area of a cube and a sphere are equal. What will be the ratio between their volume?
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- π : 6
- √π : √6
- √6 : √π
- 6 : π
- π : 6
Correct Option: B
Total surface area of cube = 6x²
Surface area of sphere = 4πr²
According to question 6x² = 4πr²
⇒ r = √ | = | ||
4π | 2√x |
So, Volume of sphere = | π × | × | × | = | π × | ||||||
3 | 2√π | 2√π | 2 × √π | 3 | 8π × √π |
∴ Required ratio = | = | = √π : √6 | ||
4π × 6x³ × √6 | √6 |