Question

The difference of Total surface area and lateral surface area of a cube is 397 cm ² find its volume.​..

Answer 1

EXPLANATION.

Difference of total surface area and lateral surface area of a cube = 397 cm².

As we know that,

Formula of :

Total surface area of cube = 6a².

Lateral surface area of cube = 4a².

Using this formula in the equation, we get.

⇒ 6a² - 4a² = 397 cm².

⇒ 2a² = 397 cm².

⇒ a² = 198.5 cm².

⇒ a = √198.5 cm².

⇒ a = 14.08 cm.

As we know that,

Volume of a cube = [edge]³ = a³.

⇒ a³ = 14.08 x 14.08 x 14.08.

⇒ a = 2791.30 cm³.

Volume of a cube = 2791.30 cm³.

Answer 2

Answer:

Given :-

• The difference of total surface area and lateral surface area of a cube is 397 cm².

To Find :-

• What is the volume of a cube.

Formula Used :-

$\clubsuit$ Total Surface Area Of Cube Formula :

$\bigstar \: \: \sf\boxed{\bold{T.S.A._{(Cube)} =\: 6a^2}}\: \: \: \bigstar$

$\bigstar \: \: \sf\boxed{\bold{L.S.A._{(Cube)} =\: 4a^2}}\: \: \: \bigstar$

where,

• a = Side

Solution :-

First, we have to find the side of a cube :

Given :

• Difference of total surface area and lateral surface area = 397 cm²

According to the question by using the formula we get,

$\implies \bf T.S.A._{(Cube)} - L.S.A._{(Cube)} =\: 397$

$\implies \sf 6a^2 - 4a^2 =\: 397$

$\implies \sf 2a^2 =\: 397$

$\implies \sf a^2 =\: \dfrac{397}{2}$

$\implies \sf a^2 =\: 198.5$

$\implies \sf a =\: \sqrt{198.5}$

$\implies \sf\bold{a =\: 14.08\: cm}$

Hence, the side of a cube is 14.08 cm .

Now, we have to find the volume of a cube :

Given :

• Side = 14.08 cm

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{Volume_{(Cube)} =\: (Side)^3}}$

$\implies \sf Volume_{(Cube)} =\: (14.08)^3$

$\implies \sf Volume_{(Cube)} =\: (14.08 \times 14.08 \times 14.08)$

$\implies \sf\bold{Volume_{(Cube)} =\: 2791.31\: cm^3}$

$\therefore$ The volume of a cube is 2791.31 cm³ .