Question

The lateral surface area of a cube is 256 m2. The volume of the cube is

Answer 1

Answer:

Step-by-step explanation:

Given :-

lateral surface area of a cube = 256 m²

To Find :-

The volume of cloth

Formula to be used :-

lateral surface area of a cube = 4 x (Side)²

volume of a cube = (Side)³

Solution :-

lateral surface area of a cube = 4 x (Side)²

$\sf\implies 256 = 4\times (Side)^2\\\sf\implies (Side)^2 = \frac{256}{4} \\\sf\implies (Side)^2 = 64\\\sf\implies Side = \sqrt{64}\\ \sf\implies Side = 8 m$

$\sf Volume \: of \: a \: cube = (Side)^3\\\sf Volume \: of \: a \: cube = (8)^3\\\sf Volume \: of \: a \: cube = 8\times8\times8\\\sf Volume \: of \: a \: cube = 512 \: m^3$

Hence, the volume of the cube is 512 m³.

Answer 2

lateral surface area of cube =4a^2

LSA=4a^2

256m^2=4a^2

a^2=64

a=√64

a=8m^2

volume of the cube=a^3=8^3=512m^3