Find the total surface area of a cube with side length 7.5 cm. What is the total surface area (in sq cm)?

Introduction / Context:
This question tests the total surface area of a cube. A cube has 6 identical square faces. If the side length is a, the area of one face is a^2, and total surface area is 6*a^2. Since a is given as 7.5 cm, we square 7.5 to get the area of one face in sq cm, then multiply by 6. The arithmetic involves decimals, so it helps to compute 7.5^2 carefully. The final answer should be in square centimetres because the input length is in centimetres.

Given Data / Assumptions:

• Cube side length a = 7.5 cm
• Area of one face = a^2
• Total surface area = 6*a^2

Concept / Approach:
Compute a^2 and multiply by 6: TSA = 6*(7.5^2). Keep units as sq cm.

Step-by-Step Solution:
a^2 = 7.5 * 7.5 = 56.25 Total surface area = 6 * 56.25 6 * 56.25 = 337.5 So TSA = 337.5 sq cm

Verification / Alternative check:
Since 7.5 is close to 8, the surface area should be close to 6*8^2 = 6*64 = 384. Our value 337.5 is smaller, which makes sense because 7.5 is smaller than 8. This sanity check supports the computed result.

Why Other Options Are Wrong:
364.5 and 446 are inconsistent with 6*a^2 for a=7.5. 684 is roughly double 337.5 and can come from multiplying by 12 instead of 6. 450 is an unrelated distractor for rounding errors.

Common Pitfalls:
Using volume formula a^3 instead of surface area, forgetting there are 6 faces, or squaring 7.5 incorrectly.

Final Answer:
The total surface area is 337.5 sq cm.