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# A lateral surface area of a cube is 256 m^{2}. Find its volume.

A cube is a three-dimensional shape that is made up of 6 congruent square faces.

## Answer: If the lateral surface area of a cube is 256 m^{2}, then its volume is 512 cubic meters.

The lateral area of a cube is the sum of areas of all side faces of the cube

**Explanation:**

The lateral surface area (LSA) of the cube = sum of areas of all 4 side faces.

Let the edge length of the cube be x.

LSA = x^{2} + x^{2} + x^{2} + x^{2} = 4x^{2}

Given that, LSA of the cube is 256 m^{2}

4x^{2} = 256

x^{2} = 256/4

x^{2} = 64

x = 8

Length of edge of the given cube is 8 m.

The volume of a cube is x^{3}.

The volume of cube = x^{3 }= 8^{3} = 512 m^{3}

### Thus, the volume of the given cube is 512 m^{3}.

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