Question

5. The length of diagonal of a cube is 7✓13 cm. Find its surface area​

Answer 1

Answer :-

294cm²

__________________________

Given :-

• Length of diagonal of a cube is 7√3cm.

To Find :-

• It's surface area

__________________________

Solution :-

★As we know, that the formula of diagonal of a cube is √3 a²

Let side of the cube be a

Then,

length of it's diagonal is

$d = \sqrt{a {}^{2} + a {}^{2} + a {}^{2} } = a \sqrt{3}$

Given diagonal is 7√3cm.

By comparing both,

7√3 = a√3

=> a = 7√3/√3

=> a = 7

Hence, side of the cube will be 7cm.

★ Formula of surface area of a cube is 6a².

Put the value of a in the formula.

6a²

=> 6 × 7 × 7

=> 294

∴ Surface area of the cube is 294cm².

Answer 2

Step-by-step explanation:

Given :

• Length of diagonal of a cube is 7√3cm.

Solution:

As we know, that the formula of diagonal of a cube is √3a^2

Let side of the cube be 'a'

Then,

Length of it's diagonal is

d = √a^2 + a^2 + a^2 = a√3

Given Diagonal is 7√3 cm.

By comparing both,

7√3 = a√3

=> a = 7√3/√3

=> a = 7

Hence, side of the cube will be 7cm

Formula of a surface area of a cube is 6a^2.

Put the value of 'a' in the formula.

6a^2

=> 6×7×7 = 294

Therefore, Surface area of the cube is 294cm^2.