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miwi218 chapter 9 link

7.1 **Surface area and volume** The surface area, S, and volume, v, of a right rectangular prism with length, L, width, W, and height, H, are: S=2LW+2WH+2LH and V=LWH The surface area, S, and volume, V, of a cube with sides, S, are S=6S^2 and V=S^3

7.2 **Surface area and Volume of prisms** Altitude- of a prism is a segment that has endpoints in planes containing the bases and that is perpendicular to both planes. Height- of a prism is the length of an altitude.

Surface area of right prisms- The surface area, S, of a right prism with lateral area L, base area, B, perimeter, heightP, and height, H, is- S=L+2B or S=HP+2B. Volumes of right prisms- V=BH.

Volumes of obligue Prisms- Cavalieri's principal--If two solids have equal heights and the cross sections formed by every plane parralel to the bases of both solids have equal areas, then the two solids have equal volumes.

Volume of a prism- The volume, V, of a prism with height, H, and base area, B, is-V=BH.

7.3 **Surface area and volume of pyramids**- A pyramid is a polyhedron consisting of a base, which is a polygon, and three or more lateral faces. The faces are triangles that share a single vertex, called the vetex of the pyramid. Each lateral face has one edge in common with the base, called a base edge. The intersection of the two lateral faces is a lateral edge.

The altitude of a pyramid is the perpendicular segment from the vertex to the plane of its base. The height of a pyramid is the length of its altitude. A regular polygon is a pyramid whose base is a regular polygon and whose lateral faces are congruent triangles. The slant height is the length of the altitude of a lateral face of a regular pyramid.

The surface area, S, of a regular pyramid with lateral area, L, base area, B, perimeter of its base, p, and slant height, L, is S= L+B or S=1/2Lp+B

The volume, V, of a pyramid with height, h, and base area, B, is V=1/3Bh

7.4 **Surface area and volume of cylinders** A cylinder is asolid that consists of a circular region and its translated image on a parralell plane, with a lateral surface conecting the circles. The faces formed by circular region are called the base. The altitude of a cylinder is the segment that has endpoints in the planes containing the bases. The height is the length of the altitude. The axis is the segment joining the centers of two bases. If the axis of the cylinder is perpendicular to its abse it is a right cylinder. if not then it is an oblique cylinder.

The surface area, S, of a right cylinder with lateral area, L, base area, B, radius, r, and height, h, is S=L+2B or S= 2(pie)rh+2(pie)r^2

The volume, V, of a right cylinder with raduis r, height h, and base area B, is V=Bh or V=(pie)r^2h



7.5 **Surface area and volume of cones** A cone is a three-dimensional fiqure that consists of a circular base and a curved lateral surface that connects the base to a single point not in the plane of the base, called the vertex. The altitude of a cone is the perpindicular segment from the vertex to the plane of the base. The height of the cone is the length of the altitude. If the altitude of a cone intersects the base of the cone at its center, the cone is a right cone if not it is an oblique cone.

The surface area, S, of a right cone with lateral area, L, base of area, B, radius, r, and slant height l is S=L+B or S=(pie)rl+(pie)r^2

The volume of a cone, V, with radius, r, height, h and base area B is V=1/3Bh or V=1/3(pie)r^2h.


 * 7.6-Surface area and volume of a sphere-**

A shpere is a set of all points ni a space that are the same distanse from a given point.

The volume of a shpere, V, with radius, r is V=4/3(pie)r^3

The surface area of a sphere, S with radius, r is S=4(pie)r^2




 * 7.7- Three dimensional symmetry-**

A three dimensional fiqure can be reflected across a plane just as a 2 dimensional fiqure can. If you rotate a fiqure about its axis a spital fiqure is formed.

almost everything is three dimensional

1.volume of triangular prism-

B=4,h=2

V=Bh 8 V=8

2.Surface area-(same triangular prism as above) L=4

S=L+2B 4+4*2 4+8 S=12

3.Volume of a pyramid L=5 B=6 h=3

S=L+B 5+6 S=11

4.Surface area of a pyramidV=1/3Bh 1/3 6*3 V=1/3 18 V=6

5.Volume of a cylinder- B=5 h=2 L=8

V=Bh 5*2 10 V=10

6.Surface area of a cylinder. S=L+2B 8+2*5 8+10 S=18

7.Volume of a cone.

B=8 h=2 L=4

V=1/3Bh 8*2 16 V=1/3(of)16

8.Surface area of a cone.

S=L+B 4+8 S=12

9.Volume of a sphere r=3 V=4/3(pie)r^3 3.14*9