Question

If the sum of areas of 6 surfaces of a cube be 216sq.cm.,then let us calculate the volume of a cube​

Answer 1

Answer :

• Volume of cube is 216cm³

Given :

• If the sum of areas of 6 surfaces of a cube be 216cm²

To find :

• Volume of cube

Solution :

• Let the side of cube be a

Then,

According to Question Total surface area of cube is 6a²

↝ 6a² = 216

↝ a² = 216/6

↝a² = 36

↝a = √36

↝a = 6cm

As we know that :

• volume of cube = a³

↝ 6³

↝6 × 6 × 6

↝ 216cm³

Hence Volume of cube is 216cm³

More Explanation:

• Volume of cube = a³
• surface area of cube = 6a²
• Diagonal of cube = √3a
• Edges of cube = ³√v

Answer 2

$\boxed{\fcolorbox{red}{lightblue}{Given}}$

• If the sum of areas of 6 surfaces of a cube be 216 cm².

$\boxed{\fcolorbox{red}{lightblue}{To \: find}}$

• The volume of a cube.

$\boxed{\fcolorbox{red}{lightblue}{Soluion}}$

Let,the side of the cube= a

We know that,

The total surfaces area of a cube = 6a².

Now, according to the question,

$\tt{\implies 216 = 6 {a}^{2} }$

$\tt{\implies \cancel\frac{216}{6} = {a}^{2} }$

$\tt{\implies 36 = {a}^{2} }$

$\tt{\implies {6}^{2} = {a}^{2} }$

$\tt{\implies a = 6}$

Now,

The volume of the cube = a³

Now, putting the value of ' a ' , we get,

The volume of the cube = 6³

The volume of the cube = 6×6×6

The volume of the cube = 216 cm³

Hence, the volume of the cube = 216cm³.