6.4 Density, Cross sections and Rotation

6.4 Density,

Cross sections and Rotation

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Density is found by using a formula.

Using the triangle, you need to cover up what you are looking for.

If you are looking for:

Mass, cover it up, leaving D * V

Density, cover it up, leaving M/V

Volume, cover it up, leaving M/D

Multiple Choice

Which box has a greater density?

• Box A

• Box B

Multiple Choice

What is the formula for density?

• $$Density=\ mass\cdot volume$$

• $$Density=\frac{mass}{volume}$$

• $$Density\ =\ mass+volume$$

• $$Density=\ mass-volume$$

Multiple Choice

What can you use this to find?

• density

• density and volume

• density, mass and volume

• directions to DMV

Multiple Choice

A rock has a mass of 14g and a volume of 2cm³. What is the density of the rock?

• 7 mL

• 7 g/cm³

• 28 g/cm³

• 1/7 g/cm³

Multiple Choice

What is the volume of 150 grams of lead if it has a density of 11.3 g/cm³?

• 13.27 cm³

• 1695 cm³

• .075 cm³

• 161.3 cm³

Fill in the Blank

A rectangular block of iron has the dimensions 2 x 10 x 5 cm. If iron’s density is 7.87 g/cm³,

find the weight in gms.

(just enter in the number)

Density of an Area

Density is the amount of stuff in a space. The previous problems looked at the mass in a volume

Density can also be in an area

Population Density is the number of people divided by the area in which they are in.

The Manhatten has a high poplulation density because a lot of people live in a small area

-Density of an Area

When problems mention density, but instead of mass and volume they talk about a number of things in an area...use this

Multiple Choice

Which definition best matches the term population density?

• human beings in general

• number of people in a particular volume

• A measurement of people for a specific area

• Most of the inhabitants of a particular area

Multiple Choice

There are approximately 17,620 people per square mile in New York City. If New York City is 468 square miles, approximately how many people live in New York City?

• 17,620

• 8,246,160

• 37

• .027

Fill in the Blank

A rectangular table with dimensions 48 inches by 36 inches is covered in 594,432 bacterial cells. What is the density of the bacteria per square inch? Just enter in the number

Fill in the Blank

A city has a population of 8700 people. The area of the city is approximately 6 square miles. Approximately, how many people per square mile live in the city? (just enter in the number)

Fill in the Blank

There are approximately 690 grizzly bears Yellowstone National Park giving them a density of about .2 grizzlies per square mile. What is the approximate area of the park? Just enter the number, do not round

When we slice a 3 dimensional object and pull it apart,

the cross section is the 2 dimensional shape created

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Since you are not actually slicing the object, you need to visualize what that shape would look like if it were sliced.

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Multiple Choice

Describe the cross section.

• triangle

• rectangle

• trapezoid

• square

Multiple Choice

What shape will the vertical cross -section of a cylinder be?

• Circle

• Triangle

• Rectangle

• Ellipse

Multiple Choice

What shape will the horizontal cross-section of a cone be?

• Dome

• Circle

• Pyramid

• Triangle

Multiple Choice

What shape does this cross section make?

• Circle

• Trapezoid

• Rectangle

• Parallelogram

When two dimensional shapes are rotated around an axis, they create a 3 dimensional object

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It will help you if you visual the shape rotating around, since rotating will always make a circle, it is helpful to sketch its path

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Multiple Choice

What will you get if you rotate the triangle on the dotted line

• cone

• sphere

• cylinder

• triangular prism

Multiple Choice

Find the volume of the figure created if you rotate the triangle on the dotted line

• 5π

• 4π

• 2π

• 12π

Multiple Choice

• sphere

• cylinder

• cone

• rectangular prism

Multiple Choice

• sphere

• cylinder

• cone

• rectangular prism