Select the correct answerA cube has a total surface area of 150 cm². Calculate the length of a diagonal of the cube.

Sure, here are the steps to solve the problem:

Step 1: Understand that the total surface area of a cube is given by the formula 6a², where 'a' is the length of a side.

Step 2: Set up the equation 6a² = 150 cm² to find the length of a side.

Step 3: Solve for 'a'. Divide both sides of the equation by 6 to get a² = 25 cm².

Step 4: Take the square root of both sides to solve for 'a'. This gives a = 5 cm.

Step 5: The length of a diagonal of a cube is given by the formula √3a. Substitute 'a' with 5 cm.

Step 6: Calculate √3 * 5 cm = 8.66 cm.

So, the length of a diagonal of the cube is approximately 8.66 cm.