4.B Three Volume, Mass, and Density

Question 1

When a plane crosses through a solid, a ______________ is formed.

Answer 1

two dimensional figure

Question 2

A two dimensional figure can be rotated around a __________ continuously to form a three dimensional solid

Answer 2

line

Question 3

If a plane slices across a right prism figure parallel to its base then what cross shape is formed?

Answer 3

The cross section will be the same shape and size as the base (congruent if you will)

Question 4

When a plane slices a right prism perpendicular to its base, what is true?

Answer 4

• It intersects four faces
• The cross section formed is a rectangle.

Question 5

What is true about small cross sections?

Answer 5

• When a plane only intersects one vertex than the resulting cross section is a point
• When a plane intersects a prism along one edge the resulting cross section is a line
• The least possible number of sides for a polygon intersection is a triangle.

Question 6

What is true about large cross sections?

Answer 6

The maximum number of sides in a cross section is the number of prism faces.

Question 7

What cross section shape does a plane intersecting a cylinder parallel to its base make?

Answer 7

a circle

Question 8

What shape cross section is formed when a plane intersects a cylinder perpendicular to it’s base?

Answer 8

a rectangle is formed

Question 9

What is an ellipse in a cylinder?

Answer 9

An ellipse is a cut through a cylinder that does not touch any bases but is not parallel to the base of the solid.

Question 10

What is a parabola in a cylinder?

Answer 10

A parabola is formed when a diagonal plane slices through one base of a cylinder.
A parabola looks like an ellipse but with on eend removed.

Question 11

How do you find the volume of a cylinder?

Answer 11

V = πr2(h)
(area of circular base x height)

Question 12

How do you find the area of a prism?

Answer 12

V = bh
(base x height)

Question 13

What is Cavalier’s Principle?

Answer 13

Cavalier’s Principle is a geometrical rule that states that if two figures have the same height and same cross sectional area at every point along the height, then they will have the same volume.

Question 14

(True or False)
A right cylinder and an oblique cylinder will have different volumes even if they have the same radius and height.

Answer 14

False.
According to Cavalier’s Principle if two figures have the same height and same cross sectional area at every point along the height, then they will have the same volume.

Question 15

How can you find the volume of a pyramid?

Answer 15

V = 1/3(Bh)
1/3(base area x height)
The volume of a pyramid can also be the same are 1/3 of a prism with the same base and height measurement.

Question 16

How can you find the volume of a cylinder?

Answer 16

V = πr2(h)
(circular base area x h)

Question 17

How do you figure out the volume of a cone?

Answer 17

V = 1/3(πr2h)
1/3(area of circular base x height)
- the volume of a cone can also be 1/3 of a cylinders volume if they have the same radius and height

Question 18

How do you find the volume of a sphere?

Answer 18

V = 4/3πr2

Question 19

True or False!
All circles are not similar.

Answer 19

False!
All circles are similar.

Question 20

What happens if you dilate a figure by one?

Answer 20

It will stay the exact same size.

Question 21

What happens to the areas of similar figures when they are dilated by scale factor “k”?

Answer 21

The area of the new shape will equal equal to
original area x k2 = new area

Question 22

How can you find the density of a solid?

Answer 22

D = m/v
Density = mass of solid/volume of solid

Question 23

How can you find out the population density of an area?

Answer 23

Population Density = total pop/area of land

Question 24

How can you figure out the mass of an object?

Answer 24

M = D x V
Mass = density x volume

Question 25

How can you figure out the volume of an object?

Answer 25

mass/density