1. Unit 2 Volume

2. Warm-Up Solve 1.4p + 4 + 7 = 9p -3 2. 8(2p+5) = 2(8p + 4) Solve for p

3. Homework Check

4. Volume of shapes: A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. Rectangular PrismTriangular Prism A cylinder has two circular bases.

5. If all six faces of a rectangular prism are squares, it is a cube. Remember! Height Triangular prism Rectangular prism Cylinder Base Height Base Height Base

6. VOLUME OF PRISMS AND CYLINDERS WordsWhat is the Base? Formula Prism: The volume V of a prism is the area of the base B times the height h. Rectangular Prism = Rectangle (B=l*w) Triangular Prism= Triangle ( B= ) Cylinder: The volume of a cylinder is the area of the base B times the height h. Circle B=  r 2 V = Bh V=(l*w)h V = Bh V= (  r 2 )h V = Bh

7. Find the volume of each figure to the nearest tenth. 1. A rectangular prism with base 2 cm by 5 cm and height 3 cm. = 30 cm 3 B = 2 5 = 10 cm 2 V = Bh = 10 3 Area of base Volume of a prism

8. Find the volume of the figure to the nearest tenth. B. 4 in. 12 in. = 192  602.9 in 3 B =  (4 2 ) = 16  in 2 V = Bh = 16  12 Additional Example 1B: Finding the Volume of Prisms and Cylinders Area of base Volume of a cylinder

9. Find the volume of the figure to the nearest tenth. C. 5 ft 7 ft 6 ft V = Bh = 15 7 = 105 ft 3 B = 6 5 = 15 ft 2 1212 Additional Example 1C: Finding the Volume of Prisms and Cylinders Area of base Volume of a prism

10. Ex 4 A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box.

11. Ex 5 A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume.

12. More Shapes A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles. A cone has a circular base. The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.

14. Formulas Pyramid B = base h = height V = ⅓ B ∙ h (rectangular B=lw) (triangular B= ½ bh) Cone B = base (  r 2 ) h = height V = B ∙ h V = ⅓ (  r 2 ) ∙ h

15. Example 1 Find the volume of the figure.

16. Example 2 Find the volume of the figure.

17. Example 3 Find the volume of the figure.

18. Vocabulary A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphere is a great circle.

19. Formula Sphere r = radius Hemisphere r = radius

20. Example 1 Find the volume of a sphere with radius 9 cm, both in terms of  and to the nearest hundredth of a unit.

21. Example 2 Find the volume of a sphere with radius 3 m, both in terms of  and to the nearest hundredth of a unit.

22. HW 2.14