sipbri

sibr610 link to chapter 9

7.1 Surface Area and Volume Objectives: Explore ratios of surface area to volume Develop the concepts of maximizing volume and minimizing surface area Surface Are and Volume Formula for a Right Rectangular Prism l-length w-width h-height Surface Area S=2lw +2wh+2lh Volume V=lwh Surface Area and Volume Formula for a Cube S-surface area V-volume s-sides Surface Area S=6s² Volume V=s³ go [|here] to learn more

7.2 Surface Area and Volume of Prisms Objectives: Define and use formula for finding the surface area of a right prism Define and use a formula for finding the volume of a right prism Use Cavalieri’s Principle to develop a formula for the volume of a right or oblique prism Vocab Altitude-A segment that has endpoints in the planes containing the base to a line containing the bases and is perpendicular to both planes. Height-The length of an altitude Surface Area and Volume Formula of a Right Prism L-lateral area B-base area p-perimeter h-height Surface Area S=L + 2B or S=hp + 2B Volume V = Bh Cavalieri Bonaventure 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.**
 * Cavalieri's Principle:

7.3 Surface Area and Volume of Pyramids objectives: Define and use a formula for the surface area of a regular pyramid Define and use a formule for the volume of a pyramid http://www.flickr.com/photos/hakonlo/294072373/

Vocab Pyramid-A polyhedron in which all but one of the polygonal faces intersect at a single point Base-A polyhedron Lateral Face-The faces of a prism or pyramid that arent bases Vertex of the Pyramid-Vertex that all the lateral faces share Base Edge-An edge that is part of the basr of a pyramid, each lateral face has one edge in common with the base Lateral Edge-The intersection of two lateral faces Altitude-The perpendicular segment from the vertex to the plane of the base Heigth-The length of its altitude Regular Pyramid-Base is a regular polygon and whos lateral faces are congruent ispsceles triangles Slant Heigth-The length of an altitude of a lateral face of a ragular pyramid Surface Area and Volume Formula for a Pyramid L-lateral area B-base area p-perimeter of the base l-slant heigth Surface Area S=L + B or S= 1/2 lp + B Volume V=1/3 Bh go [|here] to learn more

7.4 Surface Area and Volume of Cylinders objectives: Define and use a formula for the surface area of a right cylinder Define and use a formula for the volume of a cylinder http://www.flickr.com/photos/mcvay728/40583872/ Vocab Cyliner-A three-simensional geometric figure with parallel congruent bases. The bases can be saped like any closed plane figure and must be oriented identically. Lateral Surface-The face or surface of a solis on its sides.That is, anyface or surface that is not a base Bases-The cicular region and its translated image Alitude-A segemtn that has endpoints in the planes containing the bases and is perpendicular to both plans Height-The length of an altitude Axis-The segemtn joining the centers of the two bases Right Cylinder-The axis of the cylinder are perpendicular to the bases Oblique Cylinder-The axis of a cylinder is not perpendicular to the bases Surface Area and Volume Formula for a Right Cylinder L-lateral area B-base area r-radius h-height Surface Area S=L + 2B or S=2PIErh + 2PIEr² Volume V=Bh or V=PIEr²h go [|here] to learn more

7.5 Surface Area and Volume of Cones objectives: Define and use the formula for the surface area of a cone Define and use the formula for the volume of a cone http://www.flickr.com/photos/bip/103166603/ Vocab Cone-A 3D figure that consists of a circular base and a curved Base- Lateral Surface- Vertex- Altitude-The perpendicular segent from the vertex to the lane of the base Height-The length of the altitude Right Cone-The altitude of a cone intersects the base of the cone at its center Oblique Cone-The altitude of a cone does not intersect the base of the cone at its center Surface Area and Volume Formulas for a Cone S-surface area V-volume L-Lateral area B-base of area r-radius l-slant heighth h-height Surface Area S=L+B or S=(PI)rl+(PI)r² Volume V=1/3 BH or V=1/3 (PI)r²

7.6 Surface Area and Volume of Spheres objectives: Define and use the formule for the surface area of a shere Define and use the formula for the volume of a sphere http://www.flickr.com/photos/donnunn/17140501/ Surface Area and Volume Formulas of a Sphere Surface Area S-Surface area V-Volume r-radius Surface Area S=4(PI)r² Volume V=4/3(PI)r² go [|here] to learn more

1. volume of triangular prism sides of tringle: 6,8,10 height: 7 V=Bxh area of base (triangle) B=1/2bh B=1/2(6x8) V=(1/2bh)h (prism) V=(1/2 6x8)x7 V=168 2.Surface area of a triangular prism sides of triangle; 6,8,10 height: 7 S=hp + 2B S=7x24 + 2x24 S=216 3. Volume of pyramid formula - 1/3 bh b= 3 h=7 put numbers in 1/3(3)(7) solve 1/3(3)(7)= 7 4. Surface Area of Pyramids formula - SL + B S= 4 L= 8 B= 12 put numbers in (4)(8) + (12) solve (4)(8) + (12) = 44 5. Volume of a cylinder formula - bh b= 8 h=9 put numbers in (8)(9) solve (8)(9)= 72 6. Surface area of a cylinder formula - SL+B S= 7 L= 6 B= 2 put numbers in (7)(6)+(2) solve (7)(6)+(2) = 44 7. Volume of Cone formula - 1/3Bh B= 5 h=9 put numbers in 1/3 (5)(9) solve 1/3(5)(9) = 15 8. Surface Area of Cone formula - L+B L= 7 B= 4 put numbers in 7+ 4 solve 7+4 = 11 9. Volume of Sphere formula - 4/3(pie)r³ r= 6 put numbers in 4/3(pie)6³ solve 4/3(pie)6³ = 904.78 10. Surface Area of Sphere formula - 4(pie)r² r= 3 put numbers in 4(pie)3² solve 4(pie)3² = 113.