Question

the total surface area of a cube is 294cu.cm.Find its volume​

Answer 1

Question:-

the total surface area of a cube is 294cu.cm.Find its volume

Answer:-

• The volume of cube is 343 cm³.

To find:-

• Volume of cube

Solution:-

• Total surface area = 294 cm³

We have to find the side of cube.

$\large{ \boxed{ \mathfrak{ total \: surface \: area = 6 {a}^{2} }}}$

Where,

• a = side of cube

Now,

$\large{ \tt : \implies \: \: \: \: 6 {a}^{2} = 294}$

$\large{ \tt : \implies \: \: \: \: {a}^{2} = \frac{294}{6} }$

$\large{ \tt : \implies \: \: \: \: {a}^{2} = 49}$

$\large{ \tt : \implies \: \: \: \: a = \sqrt{49} }$

$\large{ \tt : \implies \: \: \: \: a = 7}$

• The side of cube is 7 cm

Now, we have to find the volume of cube

${ \large{ \boxed{\mathfrak{volume = {a}^{3} }}}}$

Where,

• a = side of cube

According to question,

$\large{ \tt: \implies \: \: \: \: volume = {7}^{3} }$

$\large{ \tt: \implies \: \: \: \: volume = 7 \times 7 \times 7}$

$\large{ \tt: \implies \: \: \: \: volume = 343 \: {cm}^{3} }$

Hence,

The volume of cube is 343 cm³.

Answer 2

Answer:

• Volume of cube = 343 cm³

Given:

• Total surface area of cube = 294 cm³

To Find:

• Volume of cube

Solution:

As we know,

Total surface area = a²

where,

• a = side of cube

Now,

→ 6a² = 294

→ a² = 294/6

→ a² = 49

→ a = √49

→ a = 7

Hence,

• Side of cube = 7 cm

Finding volume,

As we know,

→ Volume = a³

→ Volume = 7³

→ Volume = 7 × 7 × 7

→ Volume = 343 cm³

Hence,

• Volume of cube = 343 cm³