If a cube has a surface area of 150 cm², what is the length of one side?

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Question: If a cube has a surface area of 150 cm², what is the length of one side?

Options:

Correct Answer: 6 cm

Solution:

Surface area = 6s². Therefore, 150 = 6s², s² = 25, s = 5 cm.

If a cube has a surface area of 150 cm², what is the length of one side?

If a cube has a surface area of 150 cm², what is the length of one side?

Step 1: Understand that a cube has 6 equal square faces.
Step 2: Know that the formula for the surface area of a cube is Surface Area = 6 * (side length)².
Step 3: Set up the equation using the given surface area: 150 cm² = 6 * (side length)².
Step 4: Divide both sides of the equation by 6 to isolate (side length)²: (side length)² = 150 cm² / 6.
Step 5: Calculate 150 cm² / 6, which equals 25 cm²: (side length)² = 25 cm².
Step 6: Take the square root of both sides to find the side length: side length = √25 cm².
Step 7: Calculate the square root of 25, which is 5 cm: side length = 5 cm.

Surface Area of a Cube – The surface area of a cube is calculated using the formula SA = 6s², where s is the length of one side.
Algebraic Manipulation – The ability to rearrange equations and solve for a variable is essential in finding the side length from the surface area.