If the volume of a cube is V m 3 , its surface area is S m 2 and the length of a diagonal is d metres, prove that V = Sd.

Let side of cube = a m. By formula, Volume of cube (V) = (side) 3 = a 3 , Surface area (S) = 6(side) 2 = 6a 2 . Length of diagonal (d) = side = . ∴ Hence, proved that V = Sd.

Mathematics

If the volume of a cube is V m³, its surface area is S m² and the length of a diagonal is d metres, prove that $6\sqrt{3}$ V = Sd.

Mensuration

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Answer

Let side of cube = a m.

By formula,

Volume of cube (V) = (side)³ = a³,

Surface area (S) = 6(side)² = 6a².

Length of diagonal (d) = $\sqrt{3}$ side = $\sqrt{3}a$ .

$\Rightarrow 6\sqrt{3}V = 6\sqrt{3} \times a^3 = 6\sqrt{3}a^3 \\[1em] \Rightarrow Sd = 6a^2 \times \sqrt{3}a = 6\sqrt{3}a^3.$

∴ $6\sqrt{3} V = Sd = 6\sqrt{3}a^3.$

Hence, proved that $6\sqrt{3}$ V = Sd.

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Mathematics

If the volume of a cube is V m3, its surface area is S m2 and the length of a diagonal is d metres, prove that 636\sqrt{3}63​ V = Sd.

Mensuration

Answer

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