Question

mass = 36 g \t mass = 81 g \t mass = 48 g
volume = 6 cm³ \t volume = 9 cm³ \t volume = 8 cm³

1. which box is represented below?

a.
b.
c.
image of a rectangular box with dimensions: 1 cm (one side), 2 cm (height), 3 cm (length)

Explanation:

Step1: Calculate the volume of the box

The box is a rectangular prism, and the formula for the volume \( V \) of a rectangular prism is \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. From the diagram, \( l = 3\space cm \), \( w = 1\space cm \), \( h = 2\space cm \). So \( V=3\times1\times2 = 6\space cm^{3} \)? Wait, no, wait, maybe I misread the dimensions. Wait, looking at the diagram again: the length is 3 cm, width is 1 cm, height is 2 cm? Wait, no, maybe it's a rectangular prism with length 3 cm, width 1 cm, height 2 cm? Wait, no, let's recalculate. Wait, maybe the dimensions are length 3 cm, width 1 cm, height 2 cm? Then volume is \( 3\times1\times2 = 6\space cm^{3} \)? But wait, no, maybe I made a mistake. Wait, the table has three boxes: Box A (Mass 36g, Volume 6 cm³), Box B (Mass 81g, Volume 9 cm³), Box C (Mass 48g, Volume 8 cm³). Now, the diagram shows a box with length 3 cm, width 1 cm, height 2 cm? Wait, no, maybe the dimensions are length 3 cm, width 2 cm, height 1 cm? Wait, no, the diagram: the base is 3 cm (length), 1 cm (width), and height 2 cm. Wait, no, let's check the volume formula again. The volume of a rectangular prism is \( V = length \times width \times height \). So if the length is 3 cm, width is 1 cm, height is 2 cm, then \( V = 3\times1\times2 = 6\space cm^{3} \). Wait, but Box A has volume 6 cm³. Wait, but wait, maybe I misread the diagram. Wait, the diagram: the front face has length 3 cm (horizontal) and height 2 cm (vertical), and the depth is 1 cm (the arrow on the top left). So volume is \( 3\times1\times2 = 6\space cm^{3} \). Now, check the table: Box A has volume 6 cm³, Box B has 9 cm³, Box C has 8 cm³. So the volume of the diagram's box is 6 cm³, which matches Box A? Wait, no, wait, maybe I made a mistake. Wait, let's recalculate the volume. Wait, maybe the dimensions are 3 cm (length), 2 cm (width), and 1 cm (height)? No, the diagram shows: the bottom arrow is 3 cm (length), the right arrow is 2 cm (height), and the top left arrow is 1 cm (width). So \( V = 3\times1\times2 = 6\space cm^{3} \). So the volume is 6 cm³, which is Box A's volume (Box A: Volume = 6 cm³). Wait, but let's check again. Wait, maybe the diagram is a rectangular prism with length 3, width 2, height 1? No, the height is 2 cm, width is 1 cm, length is 3 cm. So volume is 3*1*2=6. So the box with volume 6 cm³ is Box A. Wait, but let's confirm the table:

Box A: Mass 36g, Volume 6 cm³

Box B: Mass 81g, Volume 9 cm³

Box C: Mass 48g, Volume 8 cm³

So the calculated volume is 6 cm³, which matches Box A. Wait, but maybe I messed up the dimensions. Wait, another way: maybe the box is a rectangular prism with length 3, width 2, height 1? No, the height is 2, width is 1, length is 3. So 3*1*2=6. So the volume is 6, so it's Box A. Wait, but let's check the answer options. The options are A, B, C. So the correct answer should be A? Wait, no, wait, maybe I made a mistake in the dimensions. Wait, the diagram: the length is 3 cm, the height is 2 cm, and the width (depth) is 1 cm? Or is the width 2 cm? Wait, the diagram: the front face is a rectangle with length 3 cm (horizontal) and height 2 cm (vertical), and the depth (width) is 1 cm (the arrow on the top left). So volume is 3*1*2=6. So Box A has volume 6, so the answer is A? Wait, but let's check again. Wait, maybe the dimensions are 3 cm (length), 2 cm (width), and 1 cm (height)? No, the height is 2, width is 1, length is 3. So 3*1*2=6. So yes, Box A.

Wait, but maybe I misread the diagram. Let me re-express the diagram: the box has length 3 cm, width 1 cm, height 2 cm. So volume is 3*1*2=6 cm³. So the box with volume 6 cm³ is Box A (from the table: Box A has Volume = 6 cm³). So the answer is A.

Step2: Confirm with the table

Looking at the table:

- Box A: Volume = 6 cm³

- Box B: Volume = 9 cm³

- Box C: Volume = 8 cm³

The calculated volume of the diagram's box is 6 cm³, which matches Box A's volume. So the box represented is Box A.

Answer:

A. Box A (with Mass = 36 g, Volume = 6 cm³)