### Key Concepts

A submerged object displaces a volume of liquid same to the volume of the object.One milliliter (1 mL) that water has actually a volume that 1 cubic centimeter (1cm3).Different atoms have various sizes and masses.Atoms top top the routine table are arranged in order follow to the number of protons in the nucleus.Even though an atom might be smaller than one more atom, it can have an ext mass.The fixed of atoms, your size, and also how they are arranged identify the thickness of a substance.Density equals the fixed of the object separated by its volume; D = m/v.Objects through the exact same mass however different volume have various densities.You are watching: What are limitations of the calculated and indirect volume measurement?

### Summary

Students use the water displacement an approach to discover the volume of different rods the all have actually the exact same mass. They calculate the density of every rod, and use the characteristic thickness of each material to determine all 5 rods. Then students consider the relationship in between the mass, size, and arrangement of atoms to describe why different rods have different densities. Students will be briefly presented to the regular table.

### Objective

Students will have the ability to explain the materials have characteristic densities since of the different mass, size, and arrangement of their atoms. College student will be able to use the volume displacement an approach to find the volume of an object.

### Evaluation

Download the student activity sheet, and also distribute one every student when specified in the activity. The task sheet will certainly serve together the “Evaluate” component of each 5-E lesson plan.

### Safety

Make sure you and your student wear appropriately fitting goggles.

### Materials because that Each Group

Set of 5 various rods the all have the exact same massGraduated cylinder, 100 mLWater in a cupCalculator### Notes about the materials:

For this lesson girlfriend will require a set of five solid rods, each through the exact same mass, very same diameter, but a various volume. Every rod is made of a various material. Over there are number of versions of these rods easily accessible from various suppliers. This task uses the same Mass Kit indigenous Flinn scientific (Product #AP4636) yet can be adapted to any collection of same mass rods. Due to the fact that there space only five samples in the same Mass kit, you might need 2 kits so that each group can occupational with a sample.

This graph will help you recognize each rod. Carry out not expose this details to the students. Lock will discover the identity of each rod and the station relationship in between the density and also the size of each rod later on in this lesson.

Table 1. Physics properties for solid cylinder unkowns.SampleMaterialApproximate thickness (g/cm3)Relative lengthSmallest metalShiny gray metalDark grayTall off-whiteTallest whiteBrass | 7.5 | shortest |

Aluminum | 3.0 | |

PVC | 1.4 | |

Nylon | 1.1 | |

Polyethylene | 0.94 | longest |

Engage

## Show students 5 rods that have actually the same mass however different volumes.

Show college student the five rods and explain the they all have actually the very same mass. Then host up the longest, middle-sized, and also shortest rods and remind students that they have actually the same mass.

Ask students to do a prediction:

Which rod is the most dense? the very least dense? In between?Students might reason that due to the fact that the fixed of each rod is the same, the volume of every rod must have actually something to do with its density. Some might go so far as to say that the rod v the the smallest volume must have the greatest density, since the same mass is packed right into the smallest volume. Or the the rod through the biggest volume must have the shortest density, since the exact same mass is spread out over the biggest volume.

Tell college student that prefer the cubes in the previous activity, lock will need to know the volume and mass of every of the samples. Castle will also calculate the density of every sample and use this worth to number out which product each rod is made of.

## Show an animation and demonstrate just how to measure volume utilizing the water displacement method.

Project the computer animation Water Displacement.

Play the computer animation as you show the water displacement method using a cup the water, a i graduated cylinder, and a rod, the method students will carry out in the activity. Usage the dark gray plastic sample so the students deserve to see the better.

### Volume

Demonstrate what student will execute by pouring water native a cup right into a 100-mL graduated cylinder until it reaches a elevation that will cover the sample. This is the “initial water level.”Tell students that the surface ar of water in a tube might not be totally flat. Instead, the surface may curve in a shallow U-shape called the meniscus. When measuring, read the line simply at the bottom of the meniscus.

Tilt the i graduated cylinder and slowly on slide the sample right into the water. Organize the i graduated cylinder upright. Document the level the the water. Point out that this is the “final water level.”

Tell students the you desire to find out exactly how much the water level changed. Subtract the initial water level native the final water level to find the volume that the rod.Volume that sample = final water level − early water level.

Explore## Have students calculate the thickness of five various rods and also use the characteristic home of thickness to correctly recognize them.

Note: The densities for the 3 plastics room similar, therefore students have to be very careful as soon as measuring their volume making use of the water displacement method. Also, it is complicated to measure up the volume that the smallest rod. Provide students a hint that it is between 1.5 and also 2.0 mL.

### Question to investigate

Can friend use thickness to determine all five rods?

### Materials because that each group

Set of five various rods that all have actually the same massGraduated cylinder, 100 mLWater in a cupCalculator### Teacher preparation

Use a permanent marker to mark the 5 rods v letters A, B, C, D, and E. Store track of i beg your pardon letter coincides to which sample without letting college student know. If you space using 2 or more sets of rods, be sure to note each sample that the same product with the very same letter. After ~ a group finds the volume the a sample, they have to then pass the sample to another group until all teams have found the volume the all 5 rods. For the longest sample, i m sorry floats, students deserve to use a pencil to gently press the sample simply beneath the surface of the water to measure up its full volume.### Procedure

VolumePour enough water from your cup right into the i graduated cylinder to reach a elevation that will cover the sample. Read and also record the volume. Contempt tilt the graduated cylinder and also carefully place the sample into the water. Place the graduated cylinder upright ~ above the table and also look in ~ the level that the water. If the sample floats, use a pencil come gently press the height of the sample simply under the surface of the water. Document the variety of milliliters for this final water level.Find the lot of water displaced by individually the early level the the water from the last level. This volume equates to the volume that the cylinder in cm3.

Record this volume in the chart on the task sheet.Remove the sample by putting the water earlier into her cup and also taking the sample the end of your graduated cylinder.DensityCalculate the density using the formula D = m/v. Record the density in (g/cm3).Trade samples through other teams until you have measured the volume and calculated the density of all 5 samples. Table 2. Volume, mass, and density because that unknowns A–HSampleInitial water level (mL)Final water level (mL)Volume the the rods (cm3)Mass (g)Density (g/cm3)ABCDE15.0 | ||||

15.0 | ||||

15.0 | ||||

15.0 | ||||

15.0 |

Note: The densities student calculate may not be exactly the exact same as the provided densities in the chart. Together students room working, check their worths for volume come be sure that they are using the difference between the final and also initial water levels, not just the last level.

Table 3. Volume, mass, and density because that unknowns A–HMaterialApproximate density (g/cm3)Sample (Letters A–E)BrassAluminumPVCNylonPolyethylene8.8 | |

2.7 | |

1.4 | |

1.2 | |

0.94 |

## Discuss whether students’ values for density support your predictions indigenous the beginning of the lesson.

Discuss student values for thickness for every of the samples. Suggest out that different groups may have different values for density, yet that many of the values are close to the worths in the chart.

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Ask students:

Each group measured the volume that the same samples. What are some factors that groups could have various values for density?Students should realize that little inaccuracies in measure volume deserve to account for distinctions in thickness values. One more reason is the the graduated cylinder, itself, is no perfect. So over there is constantly some uncertainty in measuring.Remind students that in the start of the class they do a prediction around the thickness of the small, medium, and long sample. College student should have actually predicted that the longest cylinder has actually the shortest density, the shortest cylinder has the greatest density, and the middle is what in between.

Ask students:

Was her prediction about the density of these 3 samples correct? have actually students look at at their chart through the values for mass, volume, and also density because that each cylinder. Have them look for a relationship between the volume and also the density. Students have to realize the the shortest cylinder has actually the greatest density and also the longest cylinder has actually the lowest density. Is it same to say the if 2 samples have actually the same mass that the one with the bigger volume will have a lower density? Yes.Why?Because the samples have the exact same mass, their quantities will provide you an idea about their densities follow to the equation D = m/v. If a bigger number for volume is in the denominator, the density will be lower. Is it fair to say that the one through the smaller sized volume will have actually a greater density? Yes.Why?If a smaller sized number because that volume is in the denominator, the thickness will be higher.