What will be the volume of a cube whose total surface area is 1944 $$\text{cm}^2$$​?

Correct option is C

Given:

Total surface area of the cube = 1944 cm².

Formula Used:

The total surface area of a cube is given by the formula:

Surface Area = $$6a^2$$​

where a is the length of one side of the cube.

The volume of a cube is given by:

Volume = $$a^3$$​

Solution:

Given the total surface area is 1944 cm², we use the formula:

​$$6a^2 = 1944$$​​

​$$a^2 = \frac{1944}{6} = 324$$​​

a $$= \sqrt{324} = 18 \, \text{cm}$$​

Volume = $$a^3 = 18^3 = 5832 \, \text{cm}^3$$​

The volume of the cube is 5832 cm³.