1. Chapter 12 Group 6 P Crowley C Prince C King K Connell

2. Prisms Bases of a Prism- Two congruent polygons found lying in parallel planes at the top and bottom of the prism Altitude of a Prism- A segment joining the two base planes as well as perpendicular to both. The altitude of a prism is also known as the height of the prism. Lateral Faces- The faces of the prism that are not its bases. These faces are parallelograms. Lateral Edges- Parallel segments that intersect adjacent lateral faces. Cube- A rectangular solid with square faces.

3. Prisms Continued… Lateral Area or L.A.- The sum of the areas of its lateral faces Total Area or T.A.- The sum of the areas of all its faces 1 st :(T.A.= L.A.+ 2B) 2 nd :(L.A.=ph) or The lateral area of a right prism equals the perimeter of a base times the height of the prism. 3 rd :(V=Bh) or The volume of a right prism equals the area of a base times the height of the prism.

4. Pyramids Vertex- Top of the pyramid which connects all the faces Base- Bottom of the Pyramid Altitude- Segment from the vertex that is perpendicular to the base. The altitude is also the height of the pyramid. Lateral Faces- The faces of the Pyramid Lateral Edges- The segments that connect one face to another. Slant Height- The height of the lateral face

5. Pyramids Continued…. 4 th (L.A.= pl) or Lateral area= half of the perimeter of base times the slant height 5 th (V= Bh) or The volume=one third the area of the base times the height of the pyramid.

6. Cylinders Altitude of a Cylinder- the segment joining the centers of the circular bases 6 th (L.A.=2 rh) or the lateral area of a cylinder equals the circumference of a base times the height. 7 th (V= h) The volume of a cylinder equals the area of a base times the height of the cylinder

7. Cones 8 th (L.A.=  rl) or The lateral area of a cone equals half the circumference of the base times the slant height 9 th (V=1/3  r 2 h) or The volume of a cone equals one third the area of the base times the height of the cone.

8. Spheres 10 th (A=4  r 2 ) or The area of a sphere equals 4  times the square of the radius 11 th (V=4/3  r 3 ) or The volume of a sphere equals 4/3  times the cube of the radius.

9. Areas and Volumes of Similar Solids Similar Solids- Solids that have the same shape but not necessarily the same size 12 th 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, lateral areas, and total areas is a 2 :b 2 3. The ratio of the volumes is a 3 :b 3

10. 34. Ratio of Volume is 8:125 To find scale factor you need to put it into linear form, which is 2:5. The ratio of heights is just a:b, so the ratio of heights is 2:5. The ratio of lateral areas is : you have to square the scale factor so you get 4:25.

11. 35. A regular square pyramid has a base of 30 in. and total area of 1920. The area of the base is only the base, which is a square, so all sides are 30 in. We use the area of a square formula and get 900 To find slant height we use this equation: 1920 = 1/2 (120)(x) + 900 1020 = 60x x= 17

12. 35. continued This was Total Area = Lateral Area + Base Area. Slant height = 17 We then plug 17 into Lateral Area Equation( L.A. = ½ (perimeter)(l) L.A.= ½(120)(17) L.A.=1/2(2040) L.A.=1020

13. 36 A cone has volume 8 cubic centimeters and height 6 cm Find its slant height. Volume of a cone equals 1/3 8 = 1/3 6 24 = 6 4= r=2 r=2 H=6 Slant height = + = 36 + 4 = 40 = x= 2 Slant height = 2 x

14. 37 The radius of a cylinder is doubled and its height is halved. How does the volume change? 1.2.

15. 38 A

16. A cone has radius 8 and height 6. Find the volume.

17. A cylinder has radius 6 and height 4 cm. Find the lateral area.

18. Find the volume of a sphere with area 9π