Homework Assignment. U8 Intro Area of Circles Review p. 3 / Volume of Cones 8.1 Volume of Cylinders Practice p. 6-7 / 10
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1 Math 8 Name Unit 8 - Volume LEARNING TARGETS I CAN solve problems involving the volume of cylinders. I CAN solve problems involving the volume of cones. I CAN solve problems involving the volume of spheres. Assign Date Section Homework Assignment U8 Intro Area of Circles Review p. 3 / Volume of Cones 8.1 Volume of Cylinders Practice p. 6-7 / Volume of Cones 8.2 Volume of Cones Practice p / Volume of Sphere 8.3 Volume of Spheres Practice p / 8 U8 Volume Review U2 Volume Quiz Review p / 8 U8 Volume Quiz
2 Unit 8 Volume of Cylinders, Cones, and Spheres Essential Question: WHY are formulas important in math and science? Lesson 8.1 Volume of Cylinders (CCSS 8.G.9) How can I solve problems involving the volume of cylinders? Lesson 8.2 Volume of Cones (CCSS 8.G.9) How can I solve problems involving the volume of cones? Lesson 8.3 Volume of Spheres (CCSS 8.G.9) How can I solve problems involving the volume of spheres? 2
3 Area of Circles REVIEW The area A of a circle equals the product of pi (π) and the square of its radius r. A = πr 2 Remember that the radius r is half of the diameter d. Example : Find the area of the circle. Use 3.14 for π. A = πr 2 Area of circle A Replace π with 3.14 and r with 5. A = 5 5 = 25 A 78.5 The area of the circle is approximately 78.5 square centimeters. Find the area of each circle. Round to the nearest tenth. Use 3.14 for π diameter = 9.4 mm 8. radius = 3 1 ft 9. radius = 8 in. 2 3
4 8.1 Volume of Cylinders (8.G.9) NOTES Volume: Cylinder: FORMULA V = Bh B = area of the base (circle) = πr 2 h = height As with prisms, the area of the base of a cylinder tells the number of cubic units in one layer. The height tells how many layers there are in the cylinder. The volume V of a cylinder with radius r is the area of the base B times the height h. V = Bh, where B = πr 2, or V = πr 2 h The area of the base of a cylinder tells the number of cubic units in one layer. The height of the cylinder tells how many layers there are. 4
5 8.1 Volume of Cylinders (8.G.9) NOTES (continued) Example Find the volume of the cylinder. Round to the nearest tenth. V πr 2 h Volume of a cylinder V π(2) 2 (5) Replace r with 2 and h with 5. V Use a calculator The volume is about 62.8 cubic inches. EXAMPLE: Find the Volume of the Cylinder. Round to the nearest tenth. 1) Given a cylinder with the radius 5cm and height 8cm. Find the volume of this cylinder. Take π as ) Find the volume of a cylinder with a height of 5 mm and a diameter of 24 mm. Take π as
6 8.1 Volume of Cylinders Practice V = πr 2 h Show all work. Remember to label your answers. Find the volume of each cylinder. Round to the nearest tenth
7 8.1 Volume of Cylinders Practice (continued) 7. WATER STORAGE A cylindrical water tank has a diameter of 5.3 meters and a height of 9 meters. What is the maximum volume that the water tank can hold? Round to the nearest tenth. 8. PACKAGING A can of corn has a diameter of 6.6 centimeters and a height of 9.9 centimeters. How much corn can the can hold? Round to the nearest tenth. 9. CONTAINERS Felisa wants to determine the maximum capacity of a cylindrical bucket that has a radius of 6 inches and a height of 12 inches. What is the capacity of Felisa s bucket? Round to the nearest tenth. 10. GLASS Antoine is designing a new, cylindrical drinking glass. If the glass has a diameter of 8 centimeters and a height of 12.8 centimeters, what is its volume? Round to the nearest tenth. 7
8 8.2 Volume of Cone (8.G.9) NOTES A cone is a three-dimensional shape with one circular base. The volume V of a cone with radius r is one third the area of the base B times the height h. V = 1 3 Bh or V = 1 3 πr2 h FORMULA V = 1 3 Bh B = area of the base (circle) = πr 2 h = height Example: Find the volume of the cone. Round to the nearest tenth. V = 1 3 πr2 h Volume of a cone V = 1 (π ) r = 6 and h = 12 V Simplify. The volume is about cubic feet. 1) Find the volume of the cone. 2) Find the volume of the cone. Round to the nearest tenth. 8
9 8.2 Volume of Cone (8.G.9) VIDEO NOTES (continued) 3. Find the volume of the cone. Write your answers in terms of pi (π). V = 1 3 πr2 h V = πr2 h 3 4. Find the volume of the cone. Round to the nearest tenth. 5. A cone-shaped paper cup is filled with water. The height of the cup is 10 centimeters and the diameter is 8 centimeters. What is the volume of the paper cup? Round to the nearest tenth. 6. April is filling six identical cones for her piñata. Each cone has a radius of 1.5 inches and a height of 9 inches. What is the total volume of the cones? Round to the nearest tenth. 9
10 8.1 Volume of Cones Practice Show all work. Remember to label your answers. Find the volume of each cone. Round to the nearest tenth V = 1 3 πr2 h V = πr2 h
11 8.1 Volume of Cones Practice (continued) 5. height: 26.8 centimeters; 6. height: 34 feet; diameter: 9.8 feet radius: 12 centimeters V = πr2 h 3 7. DESSERT Find the volume of the ice cream cone shown below. Round to the nearest tenth. 8. SALT Lecretia uses a small funnel as shown below to fill her salt shaker. Find the volume of the funnel. Round to the nearest tenth. 11
12 8.3 Volume of Sphere (8.G.9) NOTES A sphere is a set of all points in space that are a given distance from a given point. The volume V of a sphere with radius r is four thirds the product of π and the cube of the radius r. V = 4 3 πr3. Hemisphere: FORMULAS Sphere Hemisphere V = 4 3 πr3 V = 1 2 (4 3 πr3 ) Example: Find the volume of the sphere. Round to the nearest tenth. V = 4 3 πr3 Volume of a sphere V = 4 3 (π 43 ) r = 4 V Simplify. Use a calculator. The volume is about cubic feet. 1) Find the volume of the sphere. Round to the nearest tenth. 12
13 8.3 Volume of Sphere (8.G.9) NOTES (continued) Sphere V = 4 3 πr3 Hemisphere V = 1 2 (4 3 πr3 ) or V = 2 3 πr3 2) Find the volume of a hemisphere with radius 5mm. 3) Find the volume of the hemisphere with radius 8 in. 4) Find the volume of the hemisphere with diameter 2 cm. 5) Sarah is blowing up spherical balloons for her brother s birthday party. One of the balloons has a radius of 3 inches. What is the volume of the balloon? 13
14 8.3 Volume of Spheres and Hemispheres Practice Show all work. Remember to label your answers. Find the volume of each shape. Round your answers to the nearest tenth A necklace has a single pearl with a radius of 2.1 millimeters. What is the volume of the pearl? 4. GLOBE A globe has a diameter of 14 inches. Find the volume of the globe. 5. Find the volume of the northern hemisphere of a globe that has a radius of 7 inches. 14
15 8.3 Volume of Spheres and Hemispheres Practice (continued) Sphere V = 4 3 πr3 Hemisphere V = 2 3 πr3 6) Find the volume of the sphere. Round to the nearest tenth. 7) Find the volume of a hemisphere with diameter 22 cm. 8) A spherical stone in the courtyard of the National Museum of Costa Rica has a diameter of about 8 feet. Find the volume of the spherical stone. Round to the nearest tenth. 15
16 U Review Read ALL directions Carefully! USE 3.14 FOR ALL VALUES OF PI ON THIS ENTIRE REVIEW! Find the volume of each cylinder. Round to the nearest tenth as needed CONTAINERS Felisa wants to determine the maximum capacity of a cylindrical bucket that has a radius of 6 inches and a height of 12 inches. What is the capacity of Felisa s bucket? Write your answer as a decimal. Round to the nearest tenth. Find the volume of each cone. Round to the nearest tenth
17 6. ENTRYWAY The stone posts at the entry to an estate are in the shape of a cone atop a cylinder as shown below. Find the volume of stone needed to make the entire post if the height of the cylinder is four feet. Write your answer as a decimal. Round to the nearest tenth. 3 ft Find the volume of each sphere or hemisphere. Write your answer as a decimal. Round to the nearest tenth A company manufacturing glue sticks makes the glue in a container that has a cylindrical base and a hemisphere for its cap. If the base of the glue stick is 3 inches tall, and the radius is 0.5 inches, how much volume does the container use in cubic inches? Write you answer as a decimal. Round to the nearest tenth. CHALLENGE: FUEL Two fuel tanks with the dimensions shown have the same volume. What is the value of h? 17
18 8.G.9 Formulas: Use the following formulas to solve problems πr3 πr 2 h 1 3 πr2 h Find the volume of each solid. If necessary, round to the nearest tenth. Use. 1) 2) 3) 4) 5) 6) 18
19 7) Find the volume of the ice cream cone shown. The ice cream cone consists of a cone with a hemi-sphere on top. Use 3.14 for. Write your answer as a decimal. Round to the nearest tenth if necessary. 8) Find the volume of the figure shown. The figure consists of a cylinder with a cone on top. Use 3.14 for. Write your answer as a decimal. Round to the nearest tenth if necessary. 19
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