chrreb

chre118 chapter 9 link

7.1~ Surface area and Volume

SURFACE AREA: rectangular prism VOLUME SURFACE AREA: cube
 * Rectangular based prism
 * Base shape:** Rectangle, length 'L' and width 'W'
 * Area of base:** L × W
 * Perimeter of base:** 2(L+W)
 * Surface area** = 2LW + 2(L+W)H ||
 * [[image:area_96.gif link="chre118"]] ||
 * Photo from www.1728.com ||
 * V = //l × w × h//**
 * **Surface Area of a Cube = 6 a** **2** ||



7.2 ~ SURFACE AREA AND VOLUME OF PRISMS Altitude- a segement that has endpoints in the plane containing the bases and that is perpendicualr to both planes.

Height- the length of an altitude

SURFACE AREA OF A RIGHT PRISM: (b is the shape of the ends) Surface Area = Lateral area + Area of two ends (Lateral area) = (perimeter of shape **b**) * L Surface Area = (perimeter of shape **b**) * L+ 2*(Area of shape **b**)

CAVALIERI'S PRINCIPLE: If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the solids have equal volumes

VOLUME OF A PRISM: The volume of a prism with height (h) and base area (B) is V=Bh
 * Triangular** based prism:

7.3~SURFACE AREA AND VOLUME OF PYRAMIDS

A pyramid is a polyhedron with a base and three or more lateral faces. The lateraly faces are triangles that share a single vertex called the vertex of the pyramid.

A base ledge is the edge that each lateral face has in common with the base.

A lateral edge is the intersection of two lateral faces.

Altitude is the perpendicular segement from the vertex to the plane of the base. photo from www.1728.com Height is the length of its altitude.

Regular pyramid: a pyramid whose base is a regular polygon and whose lateral faces are congruent isoceles triangles.

Slant height: the length of an altitude of a lateral face of a regular pyramid.

SURFACE AREA: S=L+B or S= 1/2 lp + B


 * Pyramid**

photo from www.1728.com

VOLUME OF A PYRAMID: 1/3Bh

7.4~ SURFACE AREA AND VOLUME OF CYLINDERS

cylinder: a solid that consists of a circular region and its translated image on a parallel plane wiht a lateral surface connecting the circles.

Axis of a cylinder: the segement joining the centers of the two bases.

A Right Cylinder: if the axis of a cylinder is perpendiculer to the bases if not its an oblique cylinder

SURFACE AREA:

S=L+2B

VOLUME: V= Bh

7.5~ SURFACE AREA AND VOLUME OF CONES

Cone: A three dimensional figure that is made up of a circular base and a curved lateral surface that connects the base to a single point called the vertex.

The Altitude of a cone is the perpendicular segement from the vertex to the planr of the base. The height of a cone is the length of its altitude.

If the altitude of the cone interesects the base of the cone at the center then its a right cone. If not, then its an oblique cone.

SURFACE AREA: S=L+B or S=3.14rl+3.14r2

VOLUME: V= 1/3Bh or V=1/3 3.14r2h

7.6~SURFACE AREA AND VOLUME OF SPHERES

Sphere: the set of all points in a space that are the same distance from a given point known as the center of the sphere.

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Annulus: the circular region in the sphere.

VOLUME AND SURFACE AREA :

V= 4/3 3.14r3

S= 4 3.14r2

Triangular prism~ 1: volume: 1/2*length*width*height. 2: surface area: 2B + Ph

Cone- 3: volume:1/3(Area of Base)(height) 4: surface area:

Pyramid- 5: volume: Area of the base * Height * 1/3 6: surface area: 1/2 × Perimeter × [Side Length] + [Base Area]

Sphere- 7: volume: 4/3¶r3

8: surface area: 4*3.14*r2

9: volume: ¶r2h
 * Cylinder-

10: surface area: 2*¶r2 + 2¶rh.**