Question

the total surface area of cube is 384cm3. find the volume of cube​

Answer 1

Given:-

• $\sf{Total\: surface\: area\: of\: the\: cube = 384 {cm}^{2}}$

To find:-

• $\sf{Volume\: of\: the\: cube}$

Solution:-

We know,

$\sf{Total\: Surface\: Area\: of\: a \: cube = 6{a}^{2} \: sq.units}$

= $\sf{384 = 6{a}^{2}}$

= $\sf{\dfrac{384}{6} = {a}^{2}}$

= $\sf{64 = {a}^{2}}$

=> $\sf{a = \sqrt{64}}$

=> $\sf{a = 8\: cm}$

Now,

$\sf{Volume\:of\:a\:cube = {side}^{3}\:cubic\: units}$

= $\sf{Volume = {(8)}^{3}\:{cm}^{3}}$

= $\sf{Volume = 512 {cm}^{3}}$

$\sf{\therefore The\:Volume\:of\:the\:cube\:is\:512\:{cm}^{3}}$

Extra Information:-

• $\sf{Volume\:of\:a\:cuboid = length\times breadth\times height\:\: Cubic\:units}$
• $\sf{Lateral\:Surface\:Area\:of\:a\:cuboid = 2(Length + Breadth)\times height \:\:sq.units}$
• $\sf{Total\:Surface\:Area\:of\:a\:cuboid = 2(length\times breadth + breadth\times height + height\times length)\:\: sq.units}$
• $\sf{Volume\:of\:a\:cube = {(side)}^{3}\: cubic\:units}$
• $\sf{Lateral\:Surface\:Area\:of\:a\:cube = 4{a}^{2}\: sq.units}$
• $\sf{Total\:Surface\:Area\:of\:a\:cube = 6{a}^{2}\: sq.units}$