1. The Volume of a Geometric Solid The Volume of a Geometric Solid By Tyrissa Schroeder Pages: 529-537

2. Volume of Rectangular and Cubes Prisms  Volume- is the number of cubic units required to fill a 3- demenisional figure.  Rectangular Solid- is a solid in which all six faces are rectangles.  Cube- a solid when all six faces are squares. H H W L V=lwh, Length(width)(height) V= 7(4)(14)=392ft cubed 5 5 5 V= S^3 V= 5^3 V= 5(5)(5)=125inches cubed

3. More Geometric Solids  Cylinder- is a solid in which the bases are the circles and are perpendicular to the height.  Sphere- is a three dimensional figure made up of all points a given distance from the center. 8in 4inV= pie(r^2)(height) V= 3.14(2^2)(8)=100.48in 6cm. V= 4/3(pie)(r^3) V=4/3(3.14)(6^3)= 150.72cm

4. Composite Solids  To find the volume of a solid with a missing center such as a cube with a cylinder deleted from the center, you will find the volume of the cube then subtract the volume of the cube. Example: Example: 5m 20m V= S^3 – Pie(r^2)(20) V= 20^3 – 3.14(5^2)(20)= V= 8,000m – 1,570m= 6,430m^3

5. Word Problem  A delivery truck is 3.5 meter long and 2.5 meter wide and 2 meter high.( not including the cab) Has a large box that is 1.5 meters long, 1.4 meters wide and 1.1 meters tall. What is the Volume of the space remaining in the truck?  Solution: Find the Volume of the truck then find the volume of the box and subtract. Truck Volume= lwh, 3.5(2.5)(2)= 17.5 Truck Volume= lwh, 3.5(2.5)(2)= 17.5 Box Volume = lwh, 1.5(1.4)(1.1)= 2.31 Box Volume = lwh, 1.5(1.4)(1.1)= 2.31 17.5 – 2.31= 15.19 meters^3 17.5 – 2.31= 15.19 meters^3

6. More Practice on Geometric Solids  Rectangular Solid-  Cube- 10 ft 5 ft 8 ft V= lwh V= 10(8)(5)= 140ft^3 27 cm V= S^3 V= 27^3, 27(27)(27)= 729 cm^3

7. Cylinder and Sphere  Cylinder- What is the volume difference? Yellow Tube= 6 in tall, radius of 1in. Green Tube= 8.5 in tall, radius of 3in. Volume= Pie(r^2)(h) V= 3.14(1.5)^2(6)= 42.39in^2 V= 3.14(3)^2(8)=226.08in^2 V= 226.08 - 42.39in= 183.69 V= 184in^3 Sphere- V= 4/3(pie)(r^3)= V=4/3(3.14)(2^3)= 33.49 in^3 2 in

8. Formulas Rectangular Solid V=lwh V= 7(4)(14)= 392 ft^3 Cube V= S^3 V= 5(5)(5)= 125 in ^3 Cylinder V= Pie(radius^2)(h) V=3.14(4^2)(10)= 502.4ft ^2 Sphere V= 4/3(pie)(radius^3) V= 4/3(3.14)(3^3)= 113 mm^3 Composite Solids V= S^3 – pie(radius^2)(h) V= 17^3 – 3.14(3^2)(15)= 67.4inches^3

9. Thank you!!