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  1. The total surface area of a cube and a sphere are equal. What will be the ratio between their volume?
    1. π : 6
    2. π : √6
    3. 6 : √π
    4. 6 : π
Correct Option: B

Total surface area of cube = 6x²
Surface area of sphere = 4πr²
According to question 6x² = 4πr²

⇒ r = √
6x²
=
x√6
2√x

So, Volume of sphere =
4
π ×
x√6
×
x√6
×
x√6
=
4
π ×
6x² × x√6
32√π2√π2 × √π38π × √π

∴ Required ratio =
x³ × 3 × 8π × √π
=
π
= √π : √6
4π × 6x³ × √66



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