Question

1. can all the faces of the prism below be rectangles? explain.

3 in. 4 in.
3 in. 5 in. 4 in.
2.5 in.

1. what is the surface area?

3 in. 4 in.
3 in. 5 in. 4 in.
2.5 in.

1. determine how much plastic is used to create this cinnamon container.

4 in.
3 in. 2.5 in.

1. a sculpture measures 5 meters tall, 10.5 meters long, and 5 meters wide. draw the net of the sculpture.
2. determine the surface area of the sculpture from question 4.

Explanation:

Step1: Analyze the first prism

The prism has triangular bases. So, not all faces can be rectangles.

Step2: Calculate surface - area of the first prism

The two triangular bases have area $A_{base}=\frac{1}{2}\times3\times4 = 6$ square inches each. The three rectangular faces have areas: $A_1 = 3\times2.5=7.5$ square inches, $A_2 = 4\times2.5 = 10$ square inches, $A_3=5\times2.5 = 12.5$ square inches. The total surface area $S_1=2\times6 + 7.5+10 + 12.5=42$ square inches.

Step3: Calculate surface - area of the cinnamon container

The container is a rectangular prism. The surface - area formula for a rectangular prism is $S = 2(lw+lh+wh)$. Here, $l = 3$ inches, $w = 2.5$ inches, $h = 4$ inches. So $S_2=2(3\times2.5+3\times4 + 2.5\times4)=2(7.5 + 12+10)=2\times29.5 = 59$ square inches.

Step4: Draw the net of the sculpture (description)

The sculpture is a rectangular prism. The net will have two rectangles with dimensions $10.5\times5$, two rectangles with dimensions $5\times5$, and two rectangles with dimensions $10.5\times5$.

Step5: Calculate surface - area of the sculpture

Using the surface - area formula $S=2(lw+lh+wh)$ with $l = 10.5$ meters, $w = 5$ meters, $h = 5$ meters. $S_3=2(10.5\times5+10.5\times5+5\times5)=2(52.5+52.5 + 25)=2\times130=260$ square meters.

Answer:

1. No, because it has triangular bases.
2. 42 square inches
3. 59 square inches
4. Net has 2 rectangles of 10.5×5, 2 rectangles of 5×5, 2 rectangles of 10.5×5 (description)
5. 260 square meters