A cube has a volume of 512 cubic centimetres. Determine the area of each face of the cube.
To determine the area of each face of the cube, we first need to find the length of one of its sides. Since the volume of a cube is given by the formula V = s^3, where s is the length of its sides, we can solve for s by taking the cube root of the volume:
s = ∛512 cm^3 = 8 cm
Now that we know the length of one side of the cube is 8 cm, we can calculate the area of each of its six faces. Since each face is a square, we can use the formula for the area of a square, A = s^2:
A = 8^2 cm^2 = 64 cm^2
Therefore, the area of each face of the cube is 64 square centimetres.
To find the area of each face of the cube, we need to know the side length of the cube. Since the volume of the cube is given as 512 cubic centimeters, we can find the side length by taking the cube root of the volume.
Let's calculate it step by step:
Step 1: Use the formula for the volume of a cube:
Volume = side length * side length * side length
Given that the volume is 512 cubic centimeters, we have:
512 = side length * side length * side length
Step 2: Take the cube root of both sides to find the side length:
cube root of 512 = cube root of (side length * side length * side length)
The cube root of 512 is approximately 8.
So the side length of the cube is 8 centimeters.
Step 3: Calculate the area of each face of the cube.
Since a cube has 6 equal faces, we can find the area of one face and multiply it by 6 to get the total area.
The area of each face is given by:
Area of one face = side length * side length
= 8 cm * 8 cm
= 64 square centimeters
Therefore, the area of each face of the cube is 64 square centimeters.