Question

station b – volume of a regular shaped (flat sides) solid

1. using a ruler, measure the length, width, and height of each object. measure in either mm or cm (do not use inches). be sure to record your measurements with units in the table below. remember to measure between the smallest increments on the ruler (you can measure between each mm).
2. calculate the volume of each object using the following formula volume = length × width × height. record the volume with the correct units in the table below (cm × cm × cm = cm³).

volume of a cube
volume = l × w × h
like a rectangular solid, multiply the length, times the width times the height.
image of a cube with labels l, w, h

1. record any other observations you can make about each object in the table.

data table (be descriptive with all observations)
chart with columns: object, length, width, height, volume, observations; rows for object a, b, c with handwritten data
analysis questions (answer using complete sentences):

1. which object had the largest volume? which object had the smallest volume?

handwritten answer: object a

1. will you be able to measure the volume of all solids using this method? why or why not?

handwritten answer: yes because if you measure height, length, and width and multiply all three them and you get your volume.

1. in your own words define volume.

handwritten answer: volume is the mass inside the object.

1. look at the data table, which columns include qualitative data? which columns include quantitative da...

Explanation:

Analysis Question 1

Step1: Identify volumes

Object A: $6.25\ \text{cm}^3$, Object B: $409.6\ \text{cm}^3$ (corrected from 4090, as $6.4\times6.4\times2.1 = 6.4^2\times2.1 = 40.96\times2.1 = 86.016$? Wait, original table has Object B volume as 4090, maybe miscalculation. Wait, user's table: Object A: 2.5x2.5x2.5=15.625? Wait, user wrote 62.5? Wait, image shows Object A length 2.5cm, width 2.5cm, height 2.5cm. Volume: $2.5\times2.5\times2.5 = 15.625\ \text{cm}^3$ (user wrote 62.5, maybe typo). Object B: 6.4x6.4x2.1. $6.4\times6.4 = 40.96$, $40.96\times2.1 = 86.016\ \text{cm}^3$ (user wrote 4090, wrong). Object C: 13x5.6x1.2. $13\times5.6 = 72.8$, $72.8\times1.2 = 87.36$? Wait, user wrote 72.8. Assuming user's numbers: Object A: 62.5 (maybe 2.5x2.5x10? No, original formula is LxWxH). Wait, maybe user's calculations: Object A: 2.5x2.5=6.25, x2.5=15.625, but user wrote 62.5. Object B: 6.4x6.4=40.96, x2.1=86.016, user wrote 4090 (maybe decimal error, 6.4x6.4x21? No). Object C: 13x5x1.2=78, user wrote 72.8 (maybe 5.6? 13x5.6=72.8, x1.2=87.36). But based on user's table, volumes are: A: 62.5, B: 4090, C:72.8. So comparing 62.5, 4090, 72.8: largest is B, smallest is A? Wait, user's handwritten answer says Object A, but that's wrong. Wait, maybe I misread. Wait, Object A: 2.5x2.5x2.5=15.625, Object B: 6.4x6.4x2.1=86.016, Object C:13x5.6x1.2=87.36. So largest is C, smallest is A. But user's table has Object B volume as 4090 (maybe units? If cm, 6.4cm is 64mm, 64x64x21mm=6464=4096, 409621=86016 mm³=86.016 cm³. So user's 4090 is wrong. But based on user's written numbers: A:62.5, B:4090, C:72.8. So 4090 is largest, 62.5 is smallest (A). So the answer based on user's table (even with miscalculations) is Object B has largest (4090), Object A has smallest (62.5). But user's handwritten answer says Object A, which is incorrect. Wait, maybe the problem is to use the user's table as is. So from the table:

Object A: 62.5 cm³, Object B: 4090 cm³, Object C:72.8 cm³.

So largest is Object B, smallest is Object A.

Step2: Compare volumes

4090 > 72.8 > 62.5? Wait, 72.8 is less than 4090, but 62.5 is less than 72.8. So 4090 (B) is largest, 62.5 (A) is smallest.

This method (measuring length, width, height and using \( V = L \times W \times H \)) works only for regular - shaped solids with flat, rectangular - like faces (e.g., rectangular prisms, cubes). Irregular - shaped solids (like a rock with an uneven surface, or a sphere) do not have distinct, measurable length, width, and height in the same way. For these, other methods (like water displacement) are needed. So, we cannot measure the volume of all solids using this method because it is only applicable to regular - shaped solids with flat sides that can be described by length, width, and height.

Volume is the amount of three - dimensional space that a solid object (or a liquid/gas within a container) occupies. It describes how much "space" is taken up by the object. For a regular - shaped solid with flat sides, it can be calculated as the product of its length, width, and height, but more generally, it is the measure of the space enclosed by the object.

Answer:

The object with the largest volume is Object B (with a volume of $4090\ \text{cm}^3$), and the object with the smallest volume is Object A (with a volume of $62.5\ \text{cm}^3$) (note: there may be calculation errors in the original table, but based on the provided data, this is the comparison).

Analysis Question 2