Final answer:
To find the volume of a cube with a total surface area of 150 cm², divide the surface area by 6 to determine the area of one side, then take the square root to find the length of a side. The side length is found to be 5 cm, and the cube's volume is calculated as 125 cm³.
Step-by-step explanation:
The question has provided the total surface area of a cube (150 cm²) and asks for the volume of that cube. To find the volume, we must first find the length of one side of the cube. Since a cube has 6 equal faces, we can divide the total surface area by 6 to find the area of one face. Once we have the area of one face, we can take the square root to find the length of one side.
To calculate the side length, we divide the total surface area by 6:
Side Area = Total Surface Area / 6 = 150 cm² / 6 = 25 cm²
The side length (s) is the square root of the Side Area:
s = √(Side Area) = √(25 cm²) = 5 cm
Now that we know the side length, we can find the volume (V) of the cube using the formula V = s³:
V = s³ = (5 cm)³ = 125 cm³
Therefore, the volume of the cube is 125 cubic centimeters.