It is known from the condition that the surface area of the cube is 54 dm ^ 2. And we need to find its volume.
Let’s first recall the formula for calculating the volume of a cube:
V = a ^ 3.
Now we need to find the length of the side edge of the cube. To do this, we will apply the formula to find the surface area of a cube:
S pov. cube = 6a ^ 2.
Let us express the lateral edge from the formula:
a = √ (S / 6).
Substitute values and perform calculations:
a = √ (54/6) = √9 = 3 dm.
We substitute the values into the formula for calculating the volume:
V = 3 ^ 3 = 27 dm ^ 3.
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