A cube has a volume of 50 653 cubic metres. What is the surface area of the cube?
s^3 = 50653
s = 37
surface area = 6s^2 = 8214
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To find the surface area of a cube, you need to know the length of one side of the cube.
The volume of a cube is given by the formula V = s^3, where V represents the volume and s represents the length of one side of the cube.
In this case, you are given the volume of the cube as 50 653 cubic meters.
Now, let's find the length of one side of the cube:
s = ∛V, where ∛ denotes the cube root.
Substituting the volume V = 50 653, we have:
s = ∛50 653
Using a calculator, the cube root of 50 653 is approximately 36.850941.
Therefore, the length of one side of the cube is approximately 36.850941 meters.
Now, let's find the surface area of the cube:
The surface area of a cube is given by the formula A = 6s^2, where A represents the surface area and s represents the length of one side of the cube.
Substituting the length of one side s = 36.850941, we have:
A = 6(36.850941)^2
Calculating this expression, the surface area of the cube is approximately 12 943.33 square meters.
To find the surface area of a cube, we need to know the length of one side of the cube. Since we only have the volume, we need to find the length of the side first.
To find the length of one side of the cube, we can use the formula for the volume of a cube which is:
Volume = side length^3
Given that the volume of the cube is 50,653 cubic meters, we can solve for the length of one side:
50,653 = side length^3
To find the cube root of 50,653, we can simply take the cube root of both sides of the equation:
∛50,653 = ∛side length^3
Evaluating this, we find:
∛50,653 ≈ 37.74
So, the length of one side of the cube is approximately 37.74 meters.
Now that we know the side length of the cube, we can calculate the surface area.
The surface area of a cube is given by the formula:
Surface Area = 6 * (side length)^2
Substituting the value of the side length (37.74) into the formula, we can calculate the surface area:
Surface Area = 6 * (37.74)^2
Evaluating this expression, we find:
Surface Area ≈ 26,968.74 square meters
Therefore, the surface area of the cube is approximately 26,968.74 square meters.