Name: School: Date: Facilitator: 11.01 Exploring Solids Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges. 1. Is this a polyhedron? 2. Is this a polyhedron? 3. Is this a polyhedron? Number of Faces = Number of Faces = Number of Faces = Number of Vertices = Number of Vertices = Number of Vertices = Number of Edges = Number of Edges = Number of Edges = Describe the shape formed by the cross section. 4. The shape is a 5. The shape is a 6. The shape is a Use Euler's Theorem to find the unknown number. 7. Faces = 32 8. Faces = 9. Faces = 5 Vertices = Vertices = 6 Vertices = 5 Edges = 90 Edges = 10 Edges = 10. A solid has 6 faces, 5 triangles and 1 pentagon. Use Euler's Theorem to find the number of vertices. Vertices = Name: Date: School: Facilitator: 11.02 Surface Area of Prisms and Cylinders Find the surface area of each. 1. SA = in2 2. SA = m2 4. SA = m2 5. SA = m2 3. SA = f2 Solve for x in each. 6. SA = 320 m2 x = 7. SA = 200 f2 x = 8. SA = 1000 cm2 x = 9. Find the surface area of a right rectangular prism with a height of 4 feet, a length of 10 feet, and a width of 4 feet. Show your work. SA = f2 Show your work below. 10. Find the surface area of a right cylinder with a height of 8 centimeters and a radius of 7 centimeters. Round your answer to the nearest hundredth. Show your work. SA = cm2 Show your work below. Name: Date: School: Facilitator: 11.03 Pyramids and Cones Find the surface area of each regular pyramid. Don't forget your units in your answers! It may be necessary to use the Pythagorean Theorem to find the slant height, l. 1. SA = 2. SA = 3. SA = Find the surface area of each cone. Don't forget your units in your answers! It may be necessary to use the Pythagorean Theorem to find the slant height, l. 4. SA = 5. SA = 6. SA = 7. A regular pyramid has a height of 8 inches. Its base is an equilateral triangle with a side length of 12 inches. Find the surface area of the pyramid. Show all your work. Hint: Use to find the area of the base. SA = Show your work below. 8. A right cone has a radius of 3 feet and a height of 9 feet. Find its surface area. Show all your work. Hint: You will need to use the Pythagorean Theorem to find the slant height, l. SA = Show your work below. Name: Date: School: Facilitator: 11.04 Surface Area and Volume of Spheres Find the surface area and volume of each sphere. Be sure to include appropriate units. 1. SA = Show your work below 2. SA = Show your work below Volume = Show your work below Volume = Show your work below 3. SA = Show your work below 4. SA = Show your work below Volume = Show your work below Volume = Show your work below Name: Date: School: Facilitator: 12.05 Volume of Prisms and Cylinders Find the volume of each. 1. V = Show your work below 3. V = Show your work below The volume of each solid is given. Solve for x. V = 2420 f2 5. x = Show your work below Hint: Use the triangle as the base 2. V = Show your work below 4. V = Show your work below V = 1440 m2 6. x = Show your work below Name: Date: School: Facilitator: 12.06 Volume of Pyramids and Cones Find the volume of each pyramid or cone. Show all work for full credit. 1. V = units3 Show your work 2. V = units3 Show your work 3. V = units3 Show your work 4. V = units3 Show your work 5. The volume of the cone is 130 units3. Solve for x. x = Show your work Name: Date: School: Facilitator: 12.07 Problem Solving with Surface Area and Volume On the problems below, show all of your work for full credit. 1. A storage silo is in the shape of a cylinder with a hemisphere at the top. The total height of the silo is 35 ft. The circumference of the cylinder is 22 ft. a) Find the radius of the silo. Hint: You can find the radius of a circle when given the circumference. Use C = 2r and solve for r. r = ft. Show your work below b) Find the height of the cylindrical portion of the silo. Hint: Now that you know the radius of the hemisphere, you can find the height of the cylinder, by Total Height of Silo - Height of Hemisphere h = ft. Show your work below c) Find the volume of the cylindrical portion of the silo. Hint: Use the formula for the volume of a cylinder V = ft.3 Show your work below d) Find the volume of the hemispherical portion of the silo. Hint: Use the formula for the volume of a sphere, then divide it by 2. V = ft.3 Show your work below e) What is the total volume of the silo? Hint: Add the two volumes together V = ft.3 Show your work below 2. Joe is making a toy from a rectangular block of wood. He drills two holes, each with diameter 1.4 cm, through the block. The block of wood has length 15 cm, width 8 cm, and height 5 cm. Hint: Look back at YOUR TURN #1 a) What is the volume of the block before the holes are drilled? V = cm3 Show your work below b) What is total volume removed by the drilled holes? V = cm3 Show your work below c) What is the volume of the block after the holes are drilled? V = cm3 Show your work below Name: Date: School: Facilitator: 12.08 Similar Solids Decide whether the solids are similar. If so, determine the scale factor. 1. Are the solids similar? If so, what is the scale factor? 2. Are the solids similar? If so, what is the scale factor? The solid is similar to a larger solid with the given scale factor. Find the surface area S and V of the larger solid. Show your work for full credit. 3. Scale Factor 1 : 2 S = 208 in.2 V = 192 in.3 4. Scale Factor 3 : 4 S = 96 in.2 V = 96 in.3 Volume of Larger Solid = in.3 Show your work below. Volume of Larger Solid = in.3 Show your work below