Question

A sphere and a cube has equal surface areas. The ratio of the volume of the sphere to that of cube is​

Answer 1

Step-by-step explanation:

$Given,$

$Surface area of sphere = Surface area of cube$

$w.k.t. </p><p> Surface area of cube = 6 × a { }^{2}$

$Surface area of sphere = 4 {/} 3 π r { }^{3}$

Answer 2

$\boxed{Question} \\\\\tt$

$\tt</p><p>A ~sphere~ and~ a ~cube~ has ~equal ~surface~ areas. \\\\\tt The~ ratio ~of ~the ~volume~ of~ the~ sphere \\\\\tt ~to~ that~ of~ cube~ is \\\\\tt</p><p>$

$\boxed{Ańšwėř} \\\\\sf$

$\sf </p><p>Surface ~area ~of~ cube=6a^2 \\\\\sf </p><p>Surface ~area ~of ~sphere=4 \pi r^2 \\\\\sf </p><p>Now, A/q, \\\\\sf </p><p>6a^2=4 \pi r^2 \\\\\sf </p><p>\frac{6a^2}{4 \pi r^2} = 1</p><p></p><p>$

$</p><p>Now, the ~ratio ~of ~their ~volumes = \frac{a^3}{ \frac{4}{3} \pi r^3} \\\\\sf </p><p>= \frac{6a^2 \:x \: \frac{a} {6}} {4 \pi r^2( \frac{r} {3})} \\\\\sf </p><p>= \frac{ \frac{a} {3}} { \frac{r} {3}}</p><p>=a:r </p><p>$

The required ratio is a:r