The total length of all edges of the cube is 840 cm. Calculate the area of one face of the cube. Calculate the total area of all the faces of the cube.
Let’s first calculate how long one edge of the cube is. A cube has 12 edges, which means one edge is equal to:
840: 12 = 70 (cm) – the length of one rib.
In order to find the area of a cube face, you need to multiply a pair of any of its sides with each other, because they are all equal to each other. The formula can express it like this:
S = a²,
where a is the side of the square (the edge of the cube).
S = 70² = 4900 (cm²) – the area of one face of the cube.
A cube has 6 identical faces, so let’s calculate the total area of all faces like this:
4900 * 6 = 29400 (cm²) – the total area of all sides of the cube.
Answer: the area of one face of the cube is 4900 cm², the total area of all the faces of the cube is 29400 cm².
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