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

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

Options:

Correct Answer: 6 cm

Solution:

Surface area of a cube = 6s², so 6s² = 150 cm², thus s² = 25 cm², and s = 5 cm.

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

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

Step 1: Understand that a cube has 6 equal square faces.
Step 2: Know the formula for the surface area of a cube, which is Surface Area = 6 * (length of one side)².
Step 3: Set up the equation using the given surface area: 6s² = 150 cm².
Step 4: To find s², divide both sides of the equation by 6: s² = 150 cm² / 6.
Step 5: Calculate 150 cm² / 6, which equals 25 cm², so now we have s² = 25 cm².
Step 6: To find the length of one side (s), take the square root of 25 cm²: s = √25 cm².
Step 7: Calculate the square root of 25, which is 5, so s = 5 cm.

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