Question

cube a has side lengths of 3 cm. the expression 6 × 3² can be used to find the surface area of cube a
the side lengths of cube a are increased by 2 cm to make cube b. the expression 6 × (2 + 3)² can be used to find the
surface area of cube b
find the surface area of each cube.
cube a = □ cm²
cube b = □ cm²

Explanation:

Step1: Calculate surface area of Cube A

The formula for the surface area of a cube is \(6\times s^{2}\), where \(s\) is the side - length. For Cube A, \(s = 3\) cm.
First, calculate \(3^{2}=3\times3 = 9\).
Then, \(6\times3^{2}=6\times9\).
\(6\times9 = 54\).

Step2: Calculate surface area of Cube B

For Cube B, the side - length \(s=(2 + 3)\) cm. First, \(2+3=5\) cm.
Then, calculate \((2 + 3)^{2}=5^{2}=5\times5 = 25\).
Next, \(6\times(2 + 3)^{2}=6\times25\).
\(6\times25=150\).

Answer:

Cube \(A = 54\space cm^{2}\)
Cube \(B = 150\space cm^{2}\)