Question

the total surface area of cube is 96 cm cube . the volume of a cube is a) 8 cm b)513 cm c) 64 cm d) 27 cm​

Answer 1

surface are of cube = 6s^(2)

96=6s^(2)

96/6=s^(2)

underroot 16 =s

4=s

volime=s^(3)

=4×4×4

=64

Answer 2

Question :-

The Total surface area of a cube is 96 cm² . Then the volume of the cube is ?

Options :-

• a) 8 cm³

• b) 513 cm³

• c) 64 cm³

• d) 27 cm³

Answer :-

Given :-

The total surface area of a cube is 96 cm²

Required to find :-

• Volume of the cube ?

Formulae used :-

$\large{\leadsto{\boxed{\rm{ T.S.A. \; of \; a \; cube = 6{a}^{2}}}}}$

$\large{\leadsto{\boxed{\rm{ Volume \; of \; a \; cube = {a}^{3}}}}}$

Here,

a is the measurement of the side

Solution :-

Given that :-

Total surface area of a cube is 96 cm²

We need to find the volume of the cube .

So,

In order to find the volume of the cube we need to find the measurement of a .

By finding the measurement of the side we can find the volume using the formula .

Consider,

T.S.A. of a cube = 96 cm²

Using the formula ,

$\large{\leadsto{\boxed{\rm{ T.S.A. \; of \; a \; cube = 6{a}^{2}}}}}$

So,

T.S.A. = 96 cm²

$\longrightarrow{\tt{ 96 \; {cm}^{2} = 6 \times {a}^{2}}}$

$\longrightarrow{\tt{ 96 = 6 \times {a}^{2}}}$

$\longrightarrow{\tt{ \dfrac{96}{6} = {a}^{2}}}$

$\longrightarrow{\tt{ 16 = {a}^{2}}}$

Interchange the terms on both sides

$\longrightarrow{\tt{ {a}^{2} = 16 }}$

$\longrightarrow{\tt{ a = \sqrt{16}}}$

$\implies{\tt{ a = +4 \; or \; -4 }}$

Since the length of the cube can't be in negative .

Hence,

Side of the cube ( a ) = 4 cm

Similarly,

Using the formula,

$\large{\leadsto{\boxed{\rm{ Volume \; of \; a \; cube = {a}^{3}}}}}$

Substitute the required values

$\Rightarrow{\rm{ Volume \; of \; a \; cube = {4\; cm}^{3}}}$

$\Rightarrow{\rm{ Volume = 4 \; cm \times 4 \; cm \times 4\; cm }}$

$\Rightarrow{\rm{ Volume = 64\; {cm}^{3}}}$

$\large{\boxed{\dagger{\mathsf{Volume \; of \; a \; cube = 64 \;{cm}^{3}}}}}$

Conclusion :-

Hence,

Option - c is correct .