Question

1. a rectangular prism measures 6m (length) by 3m (width) by 3m (height) is cut into three identical pieces. find the surface area gained?

Explanation:

Step1: Identify cut's added surfaces

When cutting lengthwise into 3 pieces, we make 2 cuts. Each cut adds 2 new faces (the cross-sectional area of the prism, which is width × height).

Step2: Calculate 1 cross-section area

Area of 1 cross-section: $3m \times 3p = 9mp$

Step3: Calculate total new area

2 cuts create $2 \times 2 = 4$ new cross-sectional faces.
Total gained area: $4 \times 9mp = 36mp$

Answer:

$36mp$