Six square centimetres
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A cube with 1 cm sides has a surface area of 6 cm2 and a volume of 1 cm3.
Think about this as a dice. The dice is 1cm x 1cm x 1cm. The volume of the dice is 1 x 1 x 1. The sides of the dice are 1x1 How many sides on a cube? 6 x 1 x 1 = 6cm Surface area = 6cm Then make that into a ratio, sorry I forgot that part of the question: surface area is 6 Volume is 1 so 6:1
To tackle this you first need to know the equations for both volume and surface area. The surface area of a cube is 6x2 where x is the side length. The volume of the cube is x3. Thus x is the cube root of the volume. We can substitute this in to the surface area equation and say that the surface area of a cube is 6volume2/3 This can also be rearranged to say that the volume of the cube is (the surface area/6)1.5
The total surface area is 150mm2 and the volume of the cube 125mm3
If each edge of a cube is w, then the area of each face of the cube is w2 .Since the cube has 6 faces, its total surface area is 6w2.The volume of the cube is w3 .