2. Aim: Volume Course: Applied Geo. Do Now: What is the area, in terms of  of the shaded region in the figure below? Aim: The Third Dimension: Volume – What is it? sA. of sq. = s 2 A. of circle =  r 2 A.of shaded region = A. of sq. - A. of circle A. of s. r. = s 2 -  1/2s) 2 = s 2 -  (1/4 s 2 ) = s 2 - 1/4s 2  r = 1/2 s

3. Aim: Volume Course: Applied Geo. Perimeter & Area Perimeter Perimeter - the distance around a polygon P P = 1 + 2 + 3 + 4 Area Area - the space inside a polygon - measured in square units 1 1 sq. un. 1 1 1 1 1 1 1 1 2 3 4 units 2, in 2, miles 2, etc.

4. Aim: Volume Course: Applied Geo. Volume Volume Volume - the measure of the space inside a polyhedron - measured in cubic units. V = Bh, where B = the area of the base 1 1 1 1 cu. unit 4 1 2 8 cubic units. 27cubic units. 3 3 3 Polyhedron - three dimensional figure whose surfaces are polygons Edge – a segment that is the intersection of two faces Vertex – point where edges meet

5. Aim: Volume Course: Applied Geo. Volume Formulas Prism – a polyhedron with two congruent, parallel bases. The other faces are lateral faces. Prism w l h Rectangular B = l w Triangular B = 1/2 bh B - area of the base b Rectagular prism – V = l  w  h A triangular prism is a solid whose base is a triangle.

6. Aim: Volume Course: Applied Geo. Model Problems Find the Volume of the following polyhedron: 13 17 10 V = l w h = 17 x 13 x 10 = 2210 units 3 Prism w l h Rectangular B = l w

7. Aim: Volume Course: Applied Geo. Model Problem What is the volume of a rectangular box whose base measures 3 units by 10 units and whose height is 20 units? Prism w l h Rectangular B = l w Rectangular prism – V = l  w  h 20 3 10 V = 10  3  20 = 600 units 3

8. Aim: Volume Course: Applied Geo. Model Problem The volume of a rectangular box is 2,400 cu. units. The measurements of the base are 60 x 20. What is the height of the box? w l = 2400 units 2 2400 = 60 x 20 x h 2400 = 1200 x h 2 = h 60 h 20

9. Aim: Volume Course: Applied Geo. Model Problem The base of a triangular prism has an area of 15 cm 2 and a height of 30 cm. What is the volume of the triangular prism? Triangular prism – V = B  h V = 15cm 2  30 = 450 units 3 Triangular B = 1/2 bh B - area of the base b 30 15 cm 2

10. Aim: Volume Course: Applied Geo. Volume Formula Prism – a polyhedron with two congruent, parallel bases. The other faces are lateral faces. Cube e e e What is the volume of a cube with a side of 10 units? 10

11. Aim: Volume Course: Applied Geo. Volume Formulas Cylinder Sphere r

12. Aim: Volume Course: Applied Geo. Model Problems A cylindrical tank has a radius of 10 ft. and a height of 25 ft. What is its volume? Give your answer in terms of  Cylinder 10 ft 25 ft

13. Aim: Volume Course: Applied Geo. Volume Formulas h B = area of base of pyramid Pyramid Pyramid – 3 dimensional figure with a single base and sides that are triangles. Triangular pyramid Rectangular pyramid Pentagonal pyramid

14. Aim: Volume Course: Applied Geo. Model Problems Find the volume of the pyramid with a height of 9. 15 10 9 B = l w

15. Aim: Volume Course: Applied Geo. Volume Formula Cone Cone – a pyramid with a circle for a base What is the volume of a cone whose height is 10 units and whose base has radius 5? Express in terms of  h = 10 r = 5

16. Aim: Volume Course: Applied Geo. Model Problems The main tank at the Living Seas Aquarium at EPCOT Center in Florida is the largest enclosed tank in the world. It is a cylinder with diameter 203 ft. and height 25 ft. About how many million gallons of water does this tank hold? (1 gal. = 231 in 3 ; 1728 in 3 = 1 ft 3 ) 25 ft. 203 ft. Radius is 1/2 the diameter r = 203  2 = 101.5 ft. h = 25’

17. Aim: Volume Course: Applied Geo. A. Find the surface area of the Great Pyramid, including its base. Model Problems The Great Pyramid at Giza, Egypt, was built about 2580 B.C. as a final resting place for Pharoah Khufu. At the time it was built, its height was about 481 ft. Each edge of the square base was 756 feet long. Height 481 ft. 756 ft 756’ B. Find the volume of the Great Pyramid.

18. Aim: Volume Course: Applied Geo. Model Problems Zia is planning to landscape her backyard. The yard is a 70ft-by-60ft rectangle. She plans to put down a 4- in. layer of topsoil. She can buy bags of topsoil at $2.50 per 3-ft 3 bag, with free delivery. Or she can buy bulk topsoil for $25.00 per yd 3, plus a $20 delivery fee. Which option is less expensive. Show your calculations and explanation. (1 yd 3 = 9 ft 3 ) 70 feet 60’4”

19. Aim: Volume Course: Applied Geo. Model Problems A cylinder has be cut out of the figure below. Find the volume of the remaining figure. Round your answer to the nearest tenth. 4” 6 in.

20. Aim: Volume Course: Applied Geo. Volume Formulas

21. Aim: Volume Course: Applied Geo. Volume Formulas