sheant

LINK TO CHAPTER 9 (SHAN,23) __**Surface Area and Volume**__

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, of a cube with sides s are S=6s^2 V=s^3

__**7.2- Surface Area and Volume of Prisms**__ from flickr

Altitude- the perpendicular segment from the vertex to the plane of the base Height- the length of it's altitude Surface area of a right prism- the surface area, S, of a right prism with lateral area L, base area B, perimeter p, and height h is, S=L+2B or S=hp+2B Volume of a prism is V=Bh, B for base area and h for height Cavalieri's Principle- If two solids have equal heights and cross sections formed by every plane parallel to the bases of both solids have equal areas, then both two solids have equal volumes. Area of each base is B=1/2(2)(21)=21. Perimeter of each base is p=10+21+17=48 so the lateral area is L=hp=30(48)=1440 Thus, the surface area is S=L+2B=1440+2(21)=1440+42=1482
 * EXAMPLE**

__**7.3-Surface Areas and Volumes of Pyramids**__ from flickr

Pyramid- polyhedron consisting of a base (polygon) and three or more lateral faces Base- bottom of the pyramid (polygon) Lateral Faces- Triangles that share a single vertex Vertex of the Pyramid- the top part or point of the polyhedron that all lateral faces share as a vertex Base Edge- the egde the lateral faces have in common with the base Lateral Edge- the intersection point of two lateral faces Altitude- the perpendicular segment from the vertex to the plane of the base Height- the length of it's altitude Regular Pyramid- shape whos base is a regular polygon and whose lateral faces are congruent isosceles triangles Slant Height- length of and altitude of a lateral face of a regular pyramid Surface area of a Regular Pyramid- S=L+B or S=1/2lp+B Volume of a pyramid- V=1/3Bho The roof of a gazebo is a regular octogonal pyramid with a base edge of 4 feet and a slant height of 6 feet. Find the area of the roof. If roofing material costs $3.50 per square foot, find the cost of covering the roof with this material. area of the roof is the lateral area of the pyramid. L=1/2lp=1/2(6)(8x4)=96 sq feet 96 sq feet x $3.50 per sq foot=336.00
 * EXAMPLE**

from flickr
 * __7.4- Surface Area and Volume of Cylinders__**

Cylinder- Solid that consists of a circular region and translated image on a parallel plane with a lateral surface to connect circles Bases- faces formed by the circular region and it's translated image Altitude- segment that has endpoints in the planes and is perpendicular to both planes Height- length of and altitude Axis- segment joining the centers of the two bases Right Cylinder- if a cylinder is perpendicular to the base Oblique Cylinder- Not perpendicular to the base r is radius, h is height, base area is B, lateral area is L, Surface area of a right cylinder- S=L+2B or S=2pi+2pi^2 Volume of a cylinder- V=Bh or V=pi^2h A penny is a right cylider with a diameter of 19.05 millimeters and a thickness of 1.55 millimeters. Ignoring the raised design, estimate the surface area of a penny radius of a penny is half of the diameter, or 9.525 millimeters. Use the formula for the surface area of a right cylinder. S=2ppirh+2pir^2 S=2pi(9.525)(1.55)+2pi(9.525)^2~663.46 sq millimeters from google
 * EXAMPLE**
 * __7.5- Surface Area and Volume of Cones__**

Cone- three-dimensional figure that consists of a cicular baseand a curved lateral face that touches base at one point Base- circle surface that shape sits on Lateral Face- Curved shape that connects the base at one single point Vertex- the top of the shape Altitude- perpendicular segment from the vertex to the plane of the base Height- length of the altitude Right Cone- cone where the altitude intersects the base in the center of the shape Oblique Cone- altitude does not intersect base plane in the center Slant Height- length from the outside of he vertex to the base edge Surface area of a right cone- S=L+B or S=pirl+pir^2 Volume of a cone- V=1/3Bh or V=1/3pir^2h

from google
 * __7.6- Surface Area and Volume of Spheres__**

Sphere- a shape where all points in space are the same distance from a given point in the center radius is r Volume is V=1/3pir^2h Surface area is S= 4pir^2

1) Volume and Surface Area of a Triangle SA= 10+2x23 SA= 10+46 SA= 56 square feet V= 23x9 V= 207 feet cubed

2) Volume and Surface Area of a Pyramid SA= 1/2x5x20+15 SA= 65 square feet V= 1/3x15x7 V=35

3) Volume and Surface Area of a Cylinder SA= 8+2x12 SA= 32 square feet V=pi^2x17 V= 167.7832748 feet cubed

4) Volume and Surface Area of a Cone SA=pix4x12+pix4^2 SA=201.0619298 square feet V=1/3xpix4^2x10 V=167.5516082 feet cubed

5) Volume and Surface Area of a Sphere SA=4xpix6^2 SA=1809.557368 square feet V=1/3xpix6^2x9 V=339.2920066 feet cubed __Links__ __[|http://education.yahoo.com/homework_help/math_help/problem_list?id=minigeogt_11_1]

[|http://regentsprep.org/Regents/Math/fsolid/Solids.htm]

[|http://www.math.com/school/subject3/lessons/S3U4L2GL.html#%7CWhat]__