2.  TEKS: G2B, G3B, G6B, G8D, G11D  The student will make conjectures about 3-D figures and determine the validity using a variety of approaches.  The student will construct and justify statements about geometric figures and their properties.  The student will use nets to represent and construct 3-D figures.  The student will find surface area and volume of prisms, cylinders, cones, pyramids, spheres, and composite figures.  The student will describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed.

3. The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior.

4. Find the volume of the prism. Round to the nearest tenth, if necessary. V = Bh = (bh)h Volume of a right rectangular prism V = (13)(3)(5) V = 195 cm 3 Substitute 13 for ℓ, 3 for w, and 5 for h. Simplify. Example: 1

5. Find the volume of a cube with edge length 15 in. Round to the nearest tenth, if necessary. V = s 3 Volume of a cube V = (15) 3 V = 3375 in 3 Substitute 15 for s. Simplify. Example: 2

6. Find the volume of the right regular hexagonal prism. Round to the nearest tenth, if necessary. Step 1 Remember that a regular hexagon is made of a 6 equilateral triangles. So the easiest way to find the base area B of a hexagon is to use this formula: Example: 3

7. Step 2 Use the base area to find the volume. Find the volume of the right regular hexagonal prism. Round to the nearest tenth, if necessary. Example: 3 continued

8. Find the volume of a triangular prism with a height of 9 yd whose base is a right triangle with legs 7 yd and 5 yd long. Volume of a triangular prism Substitute area of triangle formula for B Substitute numbers given Simplify Example: 4 V = Bh V = ( ½ bh) h V = ( ½)(5)(7)(9) V = 157.5 yd 3

9. A swimming pool is a rectangular prism. Estimate the volume of water in the pool in gallons when it is completely full (Hint: 1 gallon ≈ 0.134 ft 3 ). The density of water is about 8.33 pounds per gallon. Estimate the weight of the water in pounds. Example: 5

10. Step 1 Find the volume of the swimming pool in cubic feet. Step 2 Use the conversion factor to estimate the volume in gallons. V = Bh = (bh)h = (25)(15)(19) = 3375 ft 3 Example: 5 continued

11. Step 3 Use the conversion factor to estimate the weight of the water. The swimming pool holds about 25,187 gallons. The water in the swimming pool weighs about 209,804 pounds.  209,804 pounds Example: 5 continued

12. What if…? Estimate the volume in gallons and the weight of the water in the aquarium if the height were doubled. Step 1 Find the volume of the aquarium in cubic feet. V = Bh = (bh)h = (120)(60)(16) = 115,200 ft 3 Example: 6

13. Step 2 Use the conversion factor to estimate the volume in gallons. Example: 6 continued Step 3 Use the conversion factor to estimate the weight of the water. The swimming pool holds about 859,701 gallons. The water in the swimming pool weighs about 7,161,313 pounds.

14. Find the volume of the composite figure. Round to the nearest tenth. The volume of the rectangular prism is: The base area of the regular triangular prism is: V = Bh = (bh)h = (8)(4)(5) = 160 cm 3 The volume of the regular triangular prism is: The total volume of the figure is the sum of the volumes. Example: 7

15. The length, width, and height of the prism are doubled. Describe the effect on the volume. original dimensions:dimensions multiplied by 2: V = Bh V = (1.5)(4)(3) V = 18 V = Bh V = (3)(8)(6) V = 144 Doubling the dimensions increases the volume by 8 times, or increases the volume by 2 3 (the scale factor cubed for 3 dimensions). Example: 8

16. The length, width, and height of the prism are doubled. Describe the effect on the volume. original dimensions:dimensions multiplied by 2: V = Bh V = (1.5)(4)(3) V = 18 V = Bh V = (3)(8)(6) V = 144 Doubling the dimensions increases the volume by 8 times, or increases the volume by 2 3 (the scale factor cubed for 3 dimensions). Example: 9