A cube has a area of 81cm squared find its volume

Area of one face of a cube = 81 sq cm.

Hence, each side of the cube = 81^0.5 = 9 cm.

So volume of the cube = 9^3 = 729 cm^3

Step-by-step explanation:

A face of a cube must be a square, therefore:

Since area equals length times width, and a square has equal side lengths all around:

81 cm^2 = x^2 , take square root of both sides

Side length (x) = 9 cm

Now we have the length and width of the cube (9 cm each), but not the height (volume = L x W x H)

However, logically we know that the height will also be 9 cm because all six faces of the cube have side lengths of 9, so volume is 9 cm cubed

9^3 = 729 cm^3

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step-by-step explanation: