Group 6 Period 5 Problems Mac Smith, Jacob Sweeny Jack McBride

Prism- A 3 dimensional polygon Base- Congruent polygons lying on plains Altitude (Prism)- A segment joining the two base planes, it is perpendicular to both Lateral Faces- The faces of a prism that are not its bases Lateral Edges- Parallel edges that connect the bases Right Prism- A prism whose lateral faces are rectangles Oblique Prism- Any other prism^ Lateral Area (L.A.)- The sum of the areas of a prism’s lateral faces Total Area (T.A.)- The sum of the areas of all of a prism’s faces Cube- A rectangular solid with square faces

Pyramid- A 3D shape whose lateral edges meet at one point instead of the corners of a base Vertex- The point where the lateral edges of a pyramid meet Altitude (Pyramid)- The segment from the vertex that is perpendicular to the base Regular Pyramids- Pyramids with the following properties: 1)The base is a regular polygon 2)All lateral edges are congruent 3)All lateral faces are congruent isosceles triangles Slant Height- the height of a lateral face of a pyramid Cylinder- A prism whose bases are circles Right Cylinder- A cylinder whose segment joining the centers of the bases is an altitude Radius (Cylinder)- the radius of the base Cone- a pyramid whose bases are circles Similar Solids- solids with the same shape, but not necessarily same size

Formulas The formulas listen on the following slides are needed to successfully complete all problems related to Chapter 12: Areas and Volumes of Solids –NOTE: In all of the following formulas,… The term “B” denotes the area of a base of the solid figure that the formula pertains to The term “V” denotes the volume of the solid figure that the formula pertains to The term “p” denotes the perimeter of the base of the solid figure that the formula pertains to The term “l” denotes the slant height of the pyramid or cone that the formula pertains to The term “s” denotes the side length of the base of the prism or pyramid that the formula pertains to The term “r” denotes the radius of the base of the cylinder or cone that the formula pertains to The term “h” denotes the height of the prism, pyramid, cylinder or cone that the formula pertains to The term “S.A.” denotes the surface area (equal to the total area) of the prism, pyramid, cylinder, cone or sphere that the formula pertains to The term “L.A.” denotes the lateral area of the prism, pyramid, cylinder, cone or sphere that the formula pertains to The term “T.A.” denotes the total area (equal to the surface area) of the prism, pyramid, cylinder, cone or sphere that the formula pertains to

Formulas Formulas for Prisms: –The lateral area of a right prism equals the perimeter of a base times the height of the prism. (L.A. = ph) –The total area of any prism equals the lateral area of the prism plus two times the base area. (T.A. = L.A. + 2B) –The volume of a right prism equals the area of a base times the height of the prism. (V = Bh)

Formulas Formulas for Pyramids: –The lateral area of a regular pyramid equals half the perimeter of the base times the slant height. (L.A. = pl) –One can also find the lateral area of a regular pyramid with n lateral faces by finding the area of one lateral face and multiplying it by n. (L.A. = n( sl)) –The total area of any pyramid equals the lateral area of the pyramid plus the base area. (T.A. = L.A. + B) –The volume of a regular pyramid equals one third the area of the base times the height of the pyramid. (V = Bh)

Formulas Formulas for Cylinders: –The lateral area of a right cylinder equals the circumference of a base times the height of the cylinder. (L.A. = 2πrh) –The total area of any cylinder equals the lateral area of the prism plus two times the base area. (T.A. = L.A. + 2B) –The volume of a right cylinder equals the area of a base times the height of the cylinder. (V = Bh, or V = πr²h)

Formulas Formulas for Cones: –The lateral area of a right cone equals half the circumference of the base times the slant height.(L.A. = ∙ 2πr ∙ l, or L.A. = πrl) –The total area of any cone equals the lateral area of the cone plus the base area. (T.A. = L.A. + B) –The volume of a right cone equals one third the area of the base times the height of the cone. (V = πr²h)

Formulas Formulas for Spheres: –The surface area of a sphere equals 4π times the square of the radius. (S.A. = 4πr²) –The surface area of a sphere is the same as the sphere’s total area and lateral area. (S.A. = L.A. = T.A.) –The volume of a sphere equals π times the cube of the radius. (V = πr³)

Additional Theorem If the scale factor of two similar solids is “a : b,” then… 1.The ratio of corresponding perimeters is “a : b.” 2.The ratio of the base areas, of the lateral areas, and of the total areas (or the surface areas) is “a² : b².” 3.The ratio of the volumes is “a³ : b³.”

Problem 34

Problem 35

Problem 36

Problem 37 The NEW is DOUBLE the OLD in Respective VOLUMES

Problem 38