Question

Find the area and diagonal of cube whose volume is 125√9 cm cube

Answer 1

$\bold{\underline{\underline{Answer:}}}$

Area of the Cube = 314.5056 cm²

Diagonal of the cube = 12.52 cm

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :-

• Volume of Cube = 125 √9 cm³

To find :-

• Area of the cube
• Diagonal of the cube

Solution :-

We will begin with the formula for Volume of a Cube and calculate the side of the cube.

Let the edge [ Side ] of the cube be x cm.

$\implies$ $\bold{Volume\:of\:a\:cube\:=\:x^3}$

Block in the values,

$\implies$ $\bold{125\sqrt{9}\:=\:x^3}$

We can write √9 as 3,

$\implies$ $\bold{125\times3\:=\:x^3}$

$\implies$ $\bold{375\:=\:x^3}$

$\implies$ ³√375 = x

$\implies$ $\bold{7.24\:=\:x}$ [Approx.]

Side of the Cube = x = 7.24 cm

Now, let's find the area of the cube.

$\bold{Area\:of\:a\:cube\:=\:6x^2}$

Block in the values,

$\implies$ $\bold{6\times\:7.24\times\:7.24}$

$\implies$ $\bold{314.5056\:sq.cm}$

Now, let's calculate the diagonal of the cube. So, using the formula.

$\bold{Diagonal\:of\:cube\:=\sqrt{3}x}$

$\implies$ $\bold{1.73\times\:7.24}$

$\implies$ $\bold{12.5252}$

Answer 2

ANSWER:-

Given:

The volume of a cube is 125√9cm³.

To find:

•The area of a cube.

•The diagonal of a cube.

Solution:

We know that, volume of the cube= a³

So,

➞a³ = 125√9

➞a³ = 125× 3

➞a³ = 375

➞a= ³√375

➞a= 7.21cm³

Now,

⚫Area of the cube = 6a² sq. unit

➞ 6× (7.21)²

➞ 6× 51.98

➞ 311.88cm²

⚫Diagonal of a cube= √3a

➞ √3 × 7.21

➞ 1.732 × 7.21

➞ 12.487cm

Hope it helps ☺️