Question

Find the side of a cube whose surface area is 600 cm\(^2\).

• A. 6 cm
• B. 10 cm
• C. 12 cm
• D. 15 cm

Hint:

Formulas for a cube with side length \(a\): - Area of one face = \(a^2\) - Total Surface Area (TSA) = \(6a^2\) - Lateral Surface Area (LSA) = \(4a^2\) (area of the four side faces) - Volume = \(a^3\)

Answer 1

The Correct Option is B

Step 1: Recall the formula for the total surface area of a cube.
A cube has 6 equal square faces.
Let the side length of the cube be \(a\).
The area of one square face is \(a^2\).
The total surface area (TSA) of a cube is \( \text{TSA} = 6a^2 \).

Step 2: Use the given surface area to find the side length \(a\).
Given TSA = 600 cm\(^2\).
\[ 6a^2 = 600 \] \[ a^2 = \frac{600}{6} \] \[ a^2 = 100 \] \[ a = \sqrt{100} \] Since length must be positive, \( a = 10 \) cm.

Step 3: Compare with the options.
The side of the cube is 10 cm.
This matches option (2).