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Honors Geometry > Volume Unit > Flashcards

Volume Unit Flashcards

1
Q

What are all the lateral sides of a right prism?

A

Rectangles

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2
Q

What are the bases of a right prism?

A

Polygons

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3
Q

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

A

They are congruent

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4
Q

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

A

The area and perimeter of the base

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5
Q

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

A

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

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6
Q

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

A

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

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7
Q

What is the formula for Volume of a right prism?

A

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

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8
Q

What are all the lateral sides of a pyramid?

A

Isosceles triangles

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9
Q

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

A

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

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10
Q

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

A

It goes to the geometric center of the base.

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11
Q

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

A

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

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12
Q

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

A

When the base is a regular polygon.

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13
Q

What is the formula for lateral area of a pyramid?

A

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

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14
Q

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

A

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

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15
Q

What is the formula for Surface Area of a pyramid?

A

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

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16
Q

What is the formula for Volume of a pyramid?

A

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

17
Q

A cylinder is much like what other geometric shape?

A

A prism (with a circle base)

18
Q

What is the lateral side of a cylinder?

A

A rectangle

19
Q

What are the bases of a cylinder?

A

Congruent circles

20
Q

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

A

Circumference and Area of the Base.

21
Q

What is the formula for lateral area of a cylinder?

A

LA = C * h (Circumference x height)

22
Q

What is the formula for Surface Area of a cylinder?

A

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

23
Q

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?

A

A pyramid (with a circle base)

24
Q

What is the base of a cone?

A

A circle

25
Q

What is the lateral side of a cone?

A

A sector of a circle.

26
Q

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

A

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

27
Q

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

A

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

28
Q

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

A

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

29
Q

What is the formula for Surface Area of a cone?

A

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

30
Q

What is the formula for Volume of a cone?

A

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

31
Q

What is the formula for Area of a sphere?

A

A = 4πr² (A = 4 x π x radius²)

32
Q

What is the formula for volume of a sphere?

A

V = 4/3πr³ (V = 4/3 x π x radius³)

33
Q

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

A

a² : b²

34
Q

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

A

a³ : b³

35
Q

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)?

A

√a : √b

36
Q

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)?

A

∛a : ∛b

Honors Geometry (12 decks)

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