Question

The total surface area of a cube is 600 cm . the length of its diagonal is _____cm.

Answer 1

Total surface area of a cube = 6a²
So, according to the question ,
6a² = 600
A² = 100
A = 10 ......,.........root of 100 is ten
Diagonal = (√3)a
∴ length of diagonal = √3 * 10
10√3
Done

Answer 2

Given:

Total surface area of a cube,

= 600

To find:

Length of diagonal = ?

Solution:

As we know,

⇒ $Total \ surface \ area \ of \ a \ cube=6a^2$

⇒                                           $600=6a^2$

⇒                                           $\frac{600}{6}=a^2$

⇒                                            $a^2=100$

⇒                                             $a=\sqrt{100}$

⇒                                             $a=10$

Now,

The diagonal will be:

= $\sqrt{3}a$

= $\sqrt{3}\times 10$

= $\sqrt[10]{3}$

Thus, the length of its diagonal will be "$\sqrt[10]{3}$ cm",