Question

ratio of surface areas of two cubes is 25:36.find the ratio of their volumnes.​

Answer 1

$\texttt{Ratio of Surface Areas of two cubes = 25:36</p><p>}$

We know,

$\mathbb{FORMULAE \: \: FOR \: :}$

• Surface area of cube = 6a²

Now, Taking the sides of cubes as x & y.

1) $\\ \\ \\ {6x}^{2} = 25 \\ \: \: {x}^{2} = \frac{25}{6} \\ \: \: \: \:x = \sqrt{ \frac{25}{6} } = \frac{5}{ \sqrt{6} }$

2) $\\ \\ \\ {6y}^{2} = 36 \\ \: \: {y}^{2} = \frac{36}{6} = 6 \\ \: \: \: y = \sqrt{6}$

Thus,

$\sf Required \: \: Ratio = {x}^{3} : {y}^{3}$

$\rightarrow ( \frac{5}{ \sqrt{6} } )^{3} : ( \sqrt{6} )^{3} \\ \\ \rightarrow \frac{125}{6 \sqrt{6} } : 6 \sqrt{6} \\ \\ \rightarrow \frac{ \frac{125}{6 \sqrt{6} } }{6 \sqrt{6} } = \frac{125}{6 \sqrt{6}(6 \sqrt{6} ) } \\ \\ \rightarrow \frac{125}{36 \times 6} = \frac{125}{216} \\ \\ \huge \frak{ \longrightarrow \red{125 : 216}}$

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