Question

if the surface area of a cube is 294 sq. cm,then find its volume​

Answer 1

Answer:

Given:-

Surface area of a cube is 294 sq.cm

To find:-

Volume of the cube

Solution:-

We know that in a cube

$\boxed{\sf Surface\:Area=6(side)^2 }$

• substitute the values

$\qquad\quad\displaystyle\sf {:}\longrightarrow 6 (side)^2=294$

$\qquad\quad\displaystyle\sf {:}\longrightarrow (side)^2=\dfrac{294}{6}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow (side)^2=49$

$\qquad\quad\displaystyle\sf {:}\longrightarrow side=\sqrt {49}$

$\qquad\quad\displaystyle\sf {:}\longrightarrow side=7cm$

Now we know that

$\boxed{\sf Volume=(side)^3 }$

$\qquad\quad\displaystyle\sf {:}\longrightarrow Volume =7^3$

$\qquad\quad\displaystyle\sf {:}\longrightarrow Volume =343cm^3$

$\\\therefore\sf Volume\:of\:the\:cube\:is\;343cm^3 .$

Answer 2

Total surface area of cube = 6a² = 294cm²

Here a is the edge length of cube

Therefore,

Here a is the edge length of cube

6a² = 294

a² = 294/6

a² = 49

a = √49

a = 7

∴ Volume of cube = a³

= (7)³

= 343cm³