1). $\sqrt {\frac{3}{\pi }}$2). $\sqrt 3$3). \(\sqrt {\frac{\pi }{

1.	1). \(\sqrt {\frac{3}{\pi }}\)2). \(\sqrt 3\)3). \(\sqrt {\frac{\pi }{6}}\)4). \(\sqrt {\frac{6}{\pi }}\)
Answer» As we know, SURFACE area of SPHERE = 4π r², where r is the radius of sphere Surface area of cube = 6a², where a is side of cube ∴ Surface area of sphere = surface area of cube ⇒ 4πr² = 6a² $(\begin{array}{l} \Rightarrow \;\frac{{{r^2}}}{{{a^2}}} = \frac{6}{{4\pi }}\\ \Rightarrow \frac{r}{a} = \SQRT {\frac{3}{{2\pi }}}\end{array})$ Now, As we know, VOLUME of sphere = 4π r³/3, where r is the radius of sphere Volume of cube = a³, where a is side of cube ∴ (volume of sphere)/(Volume of cube) $(= \;\frac{{\frac{4}{3}\pi {r^3}}}{{{a^3}}})$ $(= \frac{{4\pi }}{3} \times {\left( {\frac{r}{a}} \right)^3} = \;\frac{{4\pi }}{3} \times {\left( {\sqrt {\frac{3}{{2\pi }}} } \right)^3} = \frac{{4\pi }}{3} \times \frac{3}{{2\pi }} \times \sqrt {\frac{3}{{2\pi }}}= \;\sqrt {\frac{6}{\pi }} )$

1). $\sqrt {\frac{3}{\pi }}$2). $\sqrt 3$3). $\sqrt {\frac{\pi }{6}}$4). $\sqrt {\frac{6}{\pi }}$

Answer»

As we know,

SURFACE area of SPHERE = 4π r², where r is the radius of sphere

Surface area of cube = 6a², where a is side of cube

∴ Surface area of sphere = surface area of cube

⇒ 4πr² = 6a²

$(\begin{array}{l} \Rightarrow \;\frac{{{r^2}}}{{{a^2}}} = \frac{6}{{4\pi }}\\ \Rightarrow \frac{r}{a} = \SQRT {\frac{3}{{2\pi }}}\end{array})$

Now,

As we know,

VOLUME of sphere = 4π r³/3, where r is the radius of sphere

Volume of cube = a³, where a is side of cube

∴ (volume of sphere)/(Volume of cube) $(= \;\frac{{\frac{4}{3}\pi {r^3}}}{{{a^3}}})$

$(= \frac{{4\pi }}{3} \times {\left( {\frac{r}{a}} \right)^3} = \;\frac{{4\pi }}{3} \times {\left( {\sqrt {\frac{3}{{2\pi }}} } \right)^3} = \frac{{4\pi }}{3} \times \frac{3}{{2\pi }} \times \sqrt {\frac{3}{{2\pi }}}= \;\sqrt {\frac{6}{\pi }} )$

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