CP1 Math 2 Unit 8: S.A., Volume, Trigonometry: Day 1 Name_______________________________ Surface Area and Volume Objectives: • Generalize a formula for volume of prisms and cylinders • Generalize a formula for surface area of cylinders • Define important vocabulary: prism, volume, surface area, cylinder, oblique, right Vocabulary VOLUME is the amount of space inside of an object. When you find the volume of a figure, you are asking, “How much stuff can this figure hold?” We measure volume in cubic units (cm3, in3, ft3, etc) because we are measuring in 3 dimensions. SURFACE AREA is the total area of the surfaces (or faces) of a 3-­‐dimensional object. Sometimes we flatten a 3-­‐dimensional figure into a 2-­‐dimensional net to find its surface area. Here is a net of a cube: We measure surface area in square units (cm2, in2, ft2, etc) because we are measuring in 2 dimensions. PRISM: a prism is a solid figure whose two end faces are congruent and parallel polygons, and whose sides are parallelograms. Which shapes below are prisms?? CYLINDER: a cylinder is a 3-­‐dimensional object with 2 circular, parallel faces. Right cylinder Oblique cylinder Prisms and cylinders can be “right” (perpendicular) or “oblique” as shown above. 1. Find the volume of the following shapes: a. A rectangular prism that measures 1 cm by 2cm by 4 cm 2 cm 1 cm 4 cm b. A cylinder with radius 12 cm and height 13cm c. A triangular prism with the given dimensions: 2. With your group, generalize a formula for finding the volume of ANY prism or cylinder. Volume of a prism or cylinder = 3. Can you write a more specific formula for the volume of a cylinder? Volume of a cylinder = 4. Here you are given the net of a general cylinder with base radius r and height h. Notice that it is made up of two circles and a rectangle. a. What is the area of one of the circles (the base of the cylinder)? b. We know the height of the rectangle is h. What is the width of the rectangle? c. What is the area of the rectangle? d. What is the surface area of the cylinder? Surface area of a cylinder = Practice: 1. Find the volume and surface area of the rectangular prism below. 2. Find the volume and surface area of the oblique cylinder below. 3. Both figures in problems 1 and 2 have a height of 24 units. Why don’t they have the same volume? Problems 4 and 5 refer to the figure below: 4. Find the total surface area (including the rectangular face) of a half cylinder with a radius of 5 inches and a height of 2 inches. 5. Find the volume of the half cylinder. In your textbook: • Section 9.10, pg. 767 #4-­‐6 • Section 7.16, pg. 612 #9-­‐12