Unit 7: 3D Figures 10.1 & D formulas & Area of Regular Polygon

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1 Unit 7: 3D Figures 10.1 & D formulas & Area of Regular Polygon NAME

2 Name the polygon with the given number of sides: 3-sided: 4-sided: 5-sided: 6-sided: 7-sided: 8-sided: 9-sided: 10-sided: Find the indicated value for each figure. 1. Parallelogram. A= 2. Trapezoid. A= 11 ft 7 ft 17 ft 3. Kite. Diagonals 12in and 18 in. 4. Cirlce. A= A= 5. Find the area of a right triangle with 6. Regular polygon. height of 4 inches across from the 60. A= A=

3 7. Rhombus. Diagonals 27 ft. and 56 ft. 8. Regular Octagon. Find the area if the apothem A = is 6 meters and side length of 5 meters. A = 9. Trapezoid. A = 231 mm 2, b 2= 10. Kite. A = 11. Circle. C = 22π 12. Regular Pentagon. Find the area if side length A = is 8 cm. A = 10.1 and 10.2 Homework: homework worksheet

4 11.1 Solid Geometry Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a. An is the segment that is the intersection of two faces. A is the point that is the intersection of three or more faces. Label the picture with the correct term! A is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.

5 Sketch each of the following solids. Triangular Prism Rectangular Prism Pentagonal Prism Hexagonal Prism Triangular Pyramid Rectangular Pyramid Pentagonal Pyramid Hexagonal Pyramid Example 1: Classify the figure. Name the vertices, edges, and bases. A is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure. To identify a three-dimensional figure from a net, look at the number of faces and the shape of each face. Example 2: Describe the three-dimensional figure that can be made from the given nets. a. b.

6 A is the intersection of a three-dimensional figure and a plane. Example 3: Describe each cross-section. a. b. c. Homework 11.1: homework worksheet

7 11.2 Volume of Prisms and Cylinders Objectives: Learn and apply the formula for the volume of a prism Learn and apply the formula for the volume of a cylinder. The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. Cavalieri s principle says that if two three-dimensional figures have the same height and have the same cross-sectional area at every level, they have the same volume. Example 1: Finding Volumes of Prisms Find the volume of the prism. Round to the nearest tenth, if necessary. B = h =

8 Example 2: Finding Volumes of Prisms Find the volume of a cube with edge length 15 in. Round to the nearest tenth, if necessary. B = h = Example 3: Finding Volumes of Prisms Find the volume of the right regular hexagonal prism. Round to the nearest tenth, if necessary. B = h = Cavalieri s principle also relates to cylinders. The two stacks have the same number of CDs, so they have the same volume.

9 Example 4: Finding Volumes of Cylinders Find the volume of the cylinder. Give your answers in terms of and rounded to the nearest tenth. B = h = Example 5: Finding Volumes of Cylinders Find the volume of a cylinder with base area 121 cm 2 and a height equal to twice the radius. Give your answer in terms of and rounded to the nearest tenth. B = h = Example 6: Finding Volumes of Composite Three-Dimensional Figures. The volume of a composite three-dimensional figure is the sum of the volumes of the individual figures. Find the volume of the composite figure. Round to the nearest tenth.

10 Find the volume of each figure. Round to the nearest tenth, if necessary. 1. a right rectangular prism with length 14 cm, width 11 cm, and height 18 cm 2. a cube with edge length 22 ft 3. a regular hexagonal prism with base edge length 10 ft and height 10 ft 4. a cylinder with diameter 16 in. and height 7 in. HOMEWORK: 11.2 homework worksheet

11 11.3 & 11.4 Volume of Pyramids, Cones & Spheres Example 1: Find the volume of each pyramid, given the height. Round to the nearest hundredth if necessary. 9 cm 10 ft B = h = B = h =

12 Example 2: Find the volume of each cone. Leave answer in terms of pi and rounded to the nearest hundredth. (HINT: slant height = 34 cm) B = h = B = h = A is the locus of points in space that are a fixed distance from a given point called the. A connects the center of the sphere to any point on the sphere. A is half of a sphere. A divides a sphere into two hemispheres.

13 What is the length of the diameter and radius of the two circles shown below? Example 3: Find the volume of each sphere. Round to the nearest tenth.. Find the volume of each figure. Round to the nearest tenth, if necessary. 1. a rectangular pyramid with length 25 cm, width 17 cm, and height 21 cm. 2. a cone with diameter 22 cm and height 30 cm. HOMEWORK: 11.3 and 11.4 homework worksheet

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