A lateral surface area of a cube is 256 m2. 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 m2, 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
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 = x2 + x2 + x2 + x2 = 4x2
Given that, LSA of the cube is 256 m2
4x2 = 256
x2 = 256/4
x2 = 64
x = 8
Length of edge of the given cube is 8 m.
The volume of a cube is x3.
The volume of cube = x3 = 83 = 512 m3
Thus, the volume of the given cube is 512 m3.