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sofia pivaral journal 9 and 10

Page history last edited by sofia pivaral 12 years, 10 months ago

_____(0-10 pts.) Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of each.

area of a square = length x width (in a square the length & width are the same, so you could multiply the side times itself.                

 

 

 

area of a rectangle = base x height


 

 

area of a triangle = 1/2bh

area of a parallelogram = bh


area of a trapezoid = (b1+b2)h / 2  b=base     h=height


area of a kite = 1/2(d1)(d2)               d= diagonal


 

 

area of a rhombus = 1/2(d1)(d2)       d=diagonal


 

 

___(0-10 pts) Describe how to find the area of a composite figure. Explain what a composite figure is. Give at least 3 examples.

A composite figure is a shape made up of simple shapes (for example triangles and rectangles), and in order to find the area of this composite figure you have to first find the area of each simple shape and add.

 

 

 

___(0-10 pts) Describe how to find the area of a circle. Give at least 3 examples.

To find the area of a circle the formula is -->  A = π r²    (r = the radius)


 

 

___(0-10 pts) Describe what a solid is. Give at least 3 examples.

A solid is a 3-Dimensional figure which can be made up of any flat or curved surfaces. 

-A flat surface in a solid = face

-The segment is a solid which is the intersection of two faces = edge

-Point which is the intersection of 3 or more of the faces = vertex


 

 

___(0-10 pts) Describe how to find the surface area of a prism. What is a prism? Explain what a “Net” is. Give at least 3 examples.

-A polyhedron (3D figure which is formed by 4 or more polygons which intersect at only one of their edges) which is formed by 2 parallel & congruent polygonal bases which are connected by lateral faces which are parallelograms. 

-A net is a diagram of the faces of any 3D figure which are arranges in a certain way that the diagram can be folded in order to create a 3D figure.

 

 

___(0-10 pts) Describe how to find the surface area of a cylinder. Give at least 3 examples.

In order to find the surface area of a cylinder you have to use the formula: 2 pi (r) (h) + 2 pi (r) squared


 

 

___(0-10 pts) Describe how to find the surface area of a pyramid. What is a pyramid? Give at least 3 examples.

A pyramid is a solid shape with triangular side faces which meet at a common point (vertex).

To find the surface area of a pyramid you have to use the formula: S = L + B

 

___(0-10 pts) Describe how to find the surface area of a cone. Give at least 3 examples.

In order to find the surface area of a cone you have to use the formula: S = pi(r) l + pi(r) squared

 

 

___(0-10 pts) Describe how to find the volume of a cube. Include a discussion about the volume postulates. Give at least 3 examples.

In order to find the volume of a cube you have to use the formula: length x width x height

 


 

___(0-10 pts) Describe Cavalieri’s principle. Give at least 3 examples.

Cavalieri's principle states that if there are two objects having the same cross-sectional area & height, then they have the same volume. 

 


 

___(0-10 pts) Describe how to find the volume of a prism. Give at least 3 examples.

To find the volume of a prism: area of the base (area of cross-section)  x height


 

 

 

___(0-10 pts) Describe how to find the volume of a cylinder. Give at least 3 examples.

There are two formulas you can use in order to find the volume of a cylinder: V = BH (base times height) or V = π r²h


 

 

 

___(0-10 pts) Describe how to find the volume of a pyramid. Give at least 3 examples.

To find the volume of a pyramid you have to use the formula: 1/3Bh



___(0-10 pts) Describe how to find the volume of a cone. Give at least 3 examples.

In order to find the volume of a cone you have to use the formula: V= 1/3Bh or V= 1/3pi "r" squared "h"


 

 

 

___(0-10 pts) Describe how to find the surface area of a sphere. Give at least 3 examples.

In order to find the surface area of a sphere you have to use the formula: S= 4 pi (r) squared


 

 

___(0-10 pts) Describe how to find the volume of a sphere. Give at least 3 examples.

In order to find the volume of a sphere you have to use the formula: V= 4/3 pi (r) cubed.


 

 

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