Volume Unit Flashcards
What are all the lateral sides of a right prism?
Rectangles
What are the bases of a right prism?
Polygons
What must be true about the two bases of any right prism?
They are congruent
When finding the lateral area, surface area, and volume of any right prism, what things should be found first?
The area and perimeter of the base
What is the formula for Lateral Area of a right prism?
LA = P * h (Perimeter of base x height)
What is the formula for Surface Area of a right prism?
SA = LA + 2B (Lateral Area + 2 x Area of Base)
What is the formula for Volume of a right prism?
V = B * h (Area of base x height)
What are all the lateral sides of a pyramid?
Isosceles triangles
When finding the lateral area, surface area, and volume of any pyramid, what things should be found first?
Perimeter of the base, Area of the base, height, slant height.
What do we know about the altitude that determines the height of a pyramid?
It goes to the geometric center of the base.
What formula is often used to find the height or slant height of a pyramid?
h² + a² = l² (height² + apothem² = slant height²)
When can the formula for Lateral Area of a pyramid be used?
When the base is a regular polygon.
What is the formula for lateral area of a pyramid?
LA = 1/2 * P * l (1/2 x perimeter of base x slant height)
How do you find the lateral area of a pyramid that is not regular?
Find the area of all the triangles and add them together.
What is the formula for Surface Area of a pyramid?
SA = LA + B (Lateral Area + Area of the Base)
What is the formula for Volume of a pyramid?
V = 1\3 * B * h (1/3 x Area of base x height)
A cylinder is much like what other geometric shape?
A prism (with a circle base)
What is the lateral side of a cylinder?
A rectangle
What are the bases of a cylinder?
Congruent circles
When finding the lateral area, surface area, and volume of any cylinder, what things should be found first?
Circumference and Area of the Base.
What is the formula for lateral area of a cylinder?
LA = C * h (Circumference x height)
What is the formula for Surface Area of a cylinder?
SA = LA + 2B (Lateral Area + 2 x Area of the Base)
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 pyramid (with a circle base)
What is the base of a cone?
A circle
What is the lateral side of a cone?
A sector of a circle.
When finding the lateral area, surface area, and volume of any cone, what things should be found first?
Circumference and Area of the base, height, slant height.
What is the formula for the lateral area of a cone?
LA = 1/2 * C * l ( 1/2 x circumference x slant height)
What formula is often used to find the height or slant height of a cone?
h² + r² = l² (height² + radius² = slant height²)
What is the formula for Surface Area of a cone?
SA = LA + B (Lateral Area + Area of Base)
What is the formula for Volume of a cone?
V = 1/3 * B * h (1/3 x Area of Base x Height)
What is the formula for Area of a sphere?
A = 4πr² (A = 4 x π x radius²)
What is the formula for volume of a sphere?
V = 4/3πr³ (V = 4/3 x π x radius³)
If the ratio of two corresponding side lengths of similar geometric solids is a:b, what is the ratio of their areas?
a² : b²
If the ratio of two corresponding side lengths of similar geometric solids is a:b, what is the ratio of their volumes?
a³ : b³
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 : √b
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 : ∛b
