Volume Unit

Question 1

What are all the lateral sides of a right prism?

Answer 1

Rectangles

Question 2

What are the bases of a right prism?

Answer 2

Polygons

Question 3

What must be true about the two bases of any right prism?

Answer 3

They are congruent

Question 4

When finding the lateral area, surface area, and volume of any right prism, what things should be found first?

Answer 4

The area and perimeter of the base

Question 5

What is the formula for Lateral Area of a right prism?

Answer 5

LA = P * h (Perimeter of base x height)

Question 6

What is the formula for Surface Area of a right prism?

Answer 6

SA = LA + 2B (Lateral Area + 2 x Area of Base)

Question 7

What is the formula for Volume of a right prism?

Answer 7

V = B * h (Area of base x height)

Question 8

What are all the lateral sides of a pyramid?

Answer 8

Isosceles triangles

Question 9

When finding the lateral area, surface area, and volume of any pyramid, what things should be found first?

Answer 9

Perimeter of the base, Area of the base, height, slant height.

Question 10

What do we know about the altitude that determines the height of a pyramid?

Answer 10

It goes to the geometric center of the base.

Question 11

What formula is often used to find the height or slant height of a pyramid?

Answer 11

h² + a² = l² (height² + apothem² = slant height²)

Question 12

When can the formula for Lateral Area of a pyramid be used?

Answer 12

When the base is a regular polygon.

Question 13

What is the formula for lateral area of a pyramid?

Answer 13

LA = 1/2 * P * l (1/2 x perimeter of base x slant height)

Question 14

How do you find the lateral area of a pyramid that is not regular?

Answer 14

Find the area of all the triangles and add them together.

Question 15

What is the formula for Surface Area of a pyramid?

Answer 15

SA = LA + B (Lateral Area + Area of the Base)

Question 16

What is the formula for Volume of a pyramid?

Answer 16

V = 1\3 * B * h (1/3 x Area of base x height)

Question 17

A cylinder is much like what other geometric shape?

Answer 17

A prism (with a circle base)

Question 18

What is the lateral side of a cylinder?

Answer 18

A rectangle

Question 19

What are the bases of a cylinder?

Answer 19

Congruent circles

Question 20

When finding the lateral area, surface area, and volume of any cylinder, what things should be found first?

Answer 20

Circumference and Area of the Base.

Question 21

What is the formula for lateral area of a cylinder?

Answer 21

LA = C * h (Circumference x height)

Question 22

What is the formula for Surface Area of a cylinder?

Answer 22

SA = LA + 2B (Lateral Area + 2 x Area of the Base)

Question 23

What is the formula for volume of a cylinder V = B * h (Area of the base x height)
A cone is much like what other geometric shape?

Answer 23

A pyramid (with a circle base)

Question 24

What is the base of a cone?

Answer 24

A circle

Question 25

What is the lateral side of a cone?

Answer 25

A sector of a circle.

Question 26

When finding the lateral area, surface area, and volume of any cone, what things should be found first?

Answer 26

Circumference and Area of the base, height, slant height.

Question 27

What is the formula for the lateral area of a cone?

Answer 27

LA = 1/2 * C * l ( 1/2 x circumference x slant height)

Question 28

What formula is often used to find the height or slant height of a cone?

Answer 28

h² + r² = l² (height² + radius² = slant height²)

Question 29

What is the formula for Surface Area of a cone?

Answer 29

SA = LA + B (Lateral Area + Area of Base)

Question 30

What is the formula for Volume of a cone?

Answer 30

V = 1/3 * B * h (1/3 x Area of Base x Height)

Question 31

What is the formula for Area of a sphere?

Answer 31

A = 4πr² (A = 4 x π x radius²)

Question 32

What is the formula for volume of a sphere?

Answer 32

V = 4/3πr³ (V = 4/3 x π x radius³)

Question 33

If the ratio of two corresponding side lengths of similar geometric solids is a:b, what is the ratio of their areas?

Answer 33

a² : b²

Question 34

If the ratio of two corresponding side lengths of similar geometric solids is a:b, what is the ratio of their volumes?

Answer 34

a³ : b³

Question 35

If the ratio of two corresponding areas of similar geometric solids is a:b, what is the ratio of their side lengths (the scale factor)?

Answer 35

√a : √b

Question 36

If the ratio of two corresponding volumes of similar geometric solids is a:b, what is the ratio of their side lengths (the scale factor)?

Answer 36

∛a : ∛b