loejac


 * loja109 chapter 9 link

7.1 Surface Area and Volume** V=volume l=length w=width h=height Surface area of a cube S=6s^2 Volume V=s^3 Rectangle Surface area and volume S=2lw+2wh+2lh V=lwh Example Theres a box with L= 10 W= 5 H=10 V=500 S=2*10*5+2*5*10+2*10*10 SA=400

Height- The height of a prism is the length of an alitude Altitude- and altitude of a prism is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes L=lateral area b=base p=perimeter h=height Surface area of a right prism S=L+ 2B or S=hp+2B Volume of a Prism V=BH Cavalier'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 two solids have equal volumes. Example- Theres a right prism with a perimeter of 50 height of 6 and a base area of 90 what is the surface area? S=6*50+2*90 S=480 and to get the volume it is V=BH V=90*6 V=540
 * 7.2 Surface Area and volume of prisms**

Pyramid- A polyhedron in which all but one of the polygonal faces intersect at a single point know as the vertex of a pyramid Base- Base is a polygon Lateral face- the faces of a prism or pyramid. Vertex of the pyramid- Lateral faces are triangles that share a single vertex Base edge- an lateral face with one edge in common with the base Lateral edge- Intersection of two lateral faces Altitude- The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base Height- The height of a pyramid is the lenght of its altitude Regular pyramid- A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles Slant height- The lenght of an altitude of a lateral face of a regular pyramid l=slant height p=perimeter h=height b=base p=perimeter Surface Area of a regular pyramid S=L+B or S=1/2lp+B Volume of a pyramid V=1/3Bh Example Theres a pyramid with a base edge of 776 feet and an height of 481. whats its volume V=1/3(776^2)(481) V=96,548,885 feet Cylinder- A cylinder is a solid that consists of a circular region Lateral surface- A lateral surface is a curved surface of a cylinder or cone Bases- Circular region and its translated image Altitude- Is a segment that was endpoints in the planes containing the bases and is perpendicular to both planes Height- Height is the lenght of an altitude Axis- of a cylinder is the segment joining the centers of the two bases right cylinder- If the axis of a cylinder is perpendicular to the bases Obligue- if its nt perpendicular
 * 7.3 Surface area and volume of pyramids**
 * 7.4 Surface area and volume of cylinders**

l=slant height p=perimeter h=height r=radius Surface area of a right cylinder formula S=2πrh+2π(r^2)

volume of a Cylinder V=π(r^2)h



Cone- a cone is a three dimensional figure that consists of a circular base and a curved lateral surface Vetex- A lateral surface that connects the bases to a single point not in the plane of the base Lateral face- Base- Altitude- The altitude of a cone is the perpendicular segment from the vertex to the plane of the base Height- the height of the cone is the length of the altitude Right cone- If the altitude of a cone intersects the base of the cone at its center. Oblique cone- If its not at the center its a oblique
 * 7.5 Surface area and volume of cones**

S=surface area r=radius l=slant height Surface area of a right cone S=πrl+πr^2 Example: Theres a cone with a radius of 5 and a slant height of 10 S=π5*10+π5^2 S=166.94 units

Volume of a cone V=1/3πr^2h Example: Theres a cone with a radius of 5 and a height of 15 V=1/3π*5^2*15 V=392.69 units Right cone- Righ coneOblique cone

Sphere- a sphere is the set of all points in space that are the same distance r from a given point know as the center of the sphere. Annulus- A ringed shaped figure in the cylinder r=radius surface area of a sphere S=4πr^2 Example: Theres a sphere with a diameter of 54 feet so the radius is 27 feet. S=4π(27)^2 4(729)π S=9160.9 square feet
 * 7.6 Volume and surface area of Spheres**

Volume of a sphere V=4/3πr^3 Example: Theres a sphere with a radius of 27 feet V=4/3π(27)^3 4/3(19,683)π V=82,488 http://mathworld.wolfram.com/Sphere.html (cool sphere site)

Help sites http://argyll.epsb.ca/jreed/math9/strand3/3107.htm http://www.regentsprep.org/Regents/math/geometry/GG2/PyramidPage.htm http://www.mathleague.com/help/geometry/3space.htm#cone

1.) Theres a right triangle with 15 cm height and a base of 5 cm V=15*5 V=75 2.) Theres a right triangle with 15 cm height and a base of 5 cm S=15*20+2*5 S=310 3.) Theres a pyramid with a slant height of 10 and a base of 5 and height of 15 V=1/3*5*15 V=25 4.) surface area of a pyramid S=1/2*10*20+5 S=105 5.) Cylinder with radius of 5 and height of 10 V=π5^2*10 V=785.39 6.) Surface area of a right cylinder S=2π*5*10+2π*5^2 S=471.23 7.)Cone that has a radius of 7 and a height of 15 and slant height of 11 V=1/3π*7^2*15 V=769.69 8.) surface area of a cone S=π*7*11+π*7^2 S=395.84 9.)Sphere with a radius of 50 V=4/3π*50^3 V=523598.77 10.) Surface area S=4π*50^2 S=31415.92