The surface area of a cube is 1728 cm$$^2$$​. Find its volume.

Correct option is B

Given:

Surface Area of cube = 1728 cm²

Formula Used:

Surface Area: $$6a^2$$​ = given surface area

Volume: $$a^3$$  

where a is the side length.

Solution:

From $$6a^2 = 1728$$​,

​$$a^2 = \frac{1728}{6} = 288$$​​

a = $$\sqrt{288} = 12\sqrt{2} cm$$​

Volume = $$(12\sqrt{2})^3$$​

=> ​$$(12)^3 \times (2)^{3/2} = 1728 \times 2\sqrt{2} = 3456\sqrt{2} \text{ cm}^3$$

Thus, the correct option is (b).