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7.2 Surface Area and Volume of Prisms

Objective: -Define and use a formula for finding the surface area of a right prism -Define and use a formula for finding the volume of a right prism -Use CavalieriÆs Principle to develop a formula for the volume of a right or oblique prism

Vocabulary: Altitude-segment that has endpoints in the planes containing the bases that are perpendicular to both planes

Height-length of an altitude

CavalieriÆs 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 the two solids have equal volumes

Formulas: Lateral formula- L=lateral area B=base area L=s h+s h+s h=h(s +s +s ) P=perimeter s ,s ,s =sides h=height Surface Area of Right Prism- S=L+2B or S=hp+2B Volume of Prism- V=Bh

Example: Find perimeter, length, and base area to solve the surface area B=1/2(3)(35)=10.75 P=12+35+15=62 L=hp=40(62)+2480 S=L+2B=2480+2(10.75)=2491.40

7.3 Surface Area and Volume of Pyramids Objective: -Define and use a formula for the surface area of a regular pyramid -Define and use a formula for the volume of a pyramid Vocabulary:

Pyramid-polyhedron consisting of a base and three or more lateral faces

Base-polygon

Lateral face-triangles that consist of the vertex of the pyramid and base edge

Vertex of Pyramid-lateral faces that share a single vertex

Base Edge-lateral faces that have one edge in common with the base

Altitude-perpendicular segment from the vertex to the plane of the base

Height-length of altitude

Slant Height-length of an altitude of a lateral face of a regular pyramid

Formulas: Surface Area of a Pyramid- S=surface area L=lateral area S=L+B or S=1/2Ip+B B=base P=perimeter I=slant height H=height

Volume of a Pyramid- V=1/3BH

Example: Find the Surface Area There is a pyramid that has a base of 5 and a lateral area of 7. S=L+B=7+5 S=12

7.4 Surface Area and Volume of Cylinders Objective: -Define and use a formula for the surface area of a right cylinder -Define and use a formula for the volume of a cylinder Vocabulary:

Cylinder-solid that consists of a circular region and itÆs

Translated image on a parallel

Lateral surface-the curved surface of a cylinder

Bases-faces formed by the circular region and its translated image

Altitude-cylinderÆs segment that has endpoints in the planes containing the bases and perpendicular to planes

Height-length of altitude

Axis-segment joining centers of the two bases

Right Cylinder-axis of cylinder is perpendicular to the bases

Oblique Cylinder-axis isnÆt perpendicular to bases

Formulas: Surface Area of Right Cylinders- S=Surface Area L=lateral base S=L+2B or S=2 rh+2 r B=Base r=Radius h=height Volume of a Cylinder- V=Bh or V= r h

Example: Find Surface Area S=2(3.14)(5)(7)+2(3.14)(25) S=6.28(35)+6.28(25) S=219.8+157 S=376.8 S=

7.5 Surface Area and Volume of Cones Objective: -Define and use the formula for the surface area of a cone -Define and use the formula for the volume of a cone

Vocabulary: Cone-3D figure that consists of a circular base and curved lateral surface that connects the base to a point

Base-circular face of a cone

Lateral surface-connects bace to a single point

Vertex-single point not in the plane of the base

Altitude-coneÆs perpendicular segment from vertex to base

Height-ConeÆs length of altitude

Right cone-altitude of cone intersects base of the cone at center

Oblique cone-altitude of cone does not intersect base of the center of the cone

Formulas: Surface Area of a Right Cone- S=surface area L=lateral area S=L+B or S= ri+ r B=Base r=Radius i=slant height h=height Volume of Cone V=1/3Bh or V=1/3 r h

Example: Find Volume V=1/3(3.14)7 (36) V=1.05(49)(36) V=51.45(36) V=1852.2

7.6 Surface Area and Volume of Spheres Objectives: -Define and use the formula for the surface area of a sphere -Define and use the formula for the volume of a sphere

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

Annulus-ring shaped figure in the cylinder0

Formulas: Volume of a Sphere- V=volume V=4/3 r r=radius Surface Area of a Sphere- S=surface area S=4 r

Example: Find the surface area and volume of the ball when the radius is three inches

V=4/3(3.14)3 V=4.18(9) V=37.62 cubic inches S=4(3.14)3 S=12.56(9) S=113.04 cubic inches