Question

7 the net of a rectangular prism and its dimensions in inches are shown.
which of the following is not a true statement about the figure?
a. when assembled, the net takes the shape of a cube.
b. all six faces are congruent.
c. the total surface area is 64 square centimeters.
d. the total surface area is 96 square centimeters.

Explanation:

Step1: Analyze Option A

A cube is a rectangular prism with all edges equal. The net has squares with side 4 cm, so when assembled, it's a cube (since all faces are squares with side 4 cm). So A is true.

Step2: Analyze Option B

Each face is a square with side 4 cm, so all six faces are congruent. B is true.

Step3: Analyze Option C and D (Surface Area)

The surface area of a cube is given by \( SA = 6s^2 \), where \( s = 4 \) cm.
Substitute \( s = 4 \):
\( SA = 6\times(4)^2 = 6\times16 = 96 \) square centimeters.
So the surface area is 96, not 64. Thus, C is false and D is true.

Answer:

C. The total surface area is 64 square centimeters.