CHAPTER 8 Geometry Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1Basic Geometric Figures 8.2Perimeter 8.3Area 8.4Circles 8.5Volume and Surface Area 8.6Relationships Between Angle Measures 8.7Congruent Triangles and Properties of Parallelograms 8.8Similar Triangles

OBJECTIVES 8.5 Volume and Surface Area Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aFind the volume and the surface area of a rectangular solid. bGiven the radius and the height, find the volume of a circular cylinder. cGiven the radius, find the volume of a sphere. dGiven the radius and the height, find the volume of a circular cone.

OBJECTIVES 8.5 Volume and Surface Area Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. eSolve applied problems involving volumes of rectangular solids, circular cylinders, spheres, and cones.

8.5 Volume and Surface Area a Find the volume and the surface area of a rectangular solid. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of a rectangular solid is the number of unit cubes needed to fill it.

8.5 Volume and Surface Area VOLUME OF A RECTANGULAR SOLID Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of a rectangular solid is found by multiplying length by width by height:

EXAMPLE 8.5 Volume and Surface Area a Find the volume and the surface area of a rectangular solid. 2Volume of a Safe Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For office security, William purchases a safe whose dimensions are 29 in. by 25 in. by 53 in. Find the volume of this rectangular solid.

8.5 Volume and Surface Area a Find the volume and the surface area of a rectangular solid. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The surface area of a rectangular solid is the total area of the six rectangles that form the surface of the solid.

8.5 Volume and Surface Area SURFACE AREA OF A RECTANGULAR SOLID Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The surface area of a rectangular solid with length l, width w, and height h is given by the formula

EXAMPLE 8.5 Volume and Surface Area a Find the volume and the surface area of a rectangular solid. 3 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the surface area of this rectangular solid.

8.5 Volume and Surface Area Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The units used for area are square units. The units used for volume are cubic units.

8.5 Volume and Surface Area VOLUME OF A CIRCULAR CYLINDER Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of a circular cylinder is the product of the area of the base B and the height h:

EXAMPLE 8.5 Volume and Surface Area b Given the radius and the height, find the volume of a circular cylinder. 4 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8.5 Volume and Surface Area c Given the radius, find the volume of a sphere. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A sphere is the three-dimensional counterpart of a circle. It is the set of all points in space that are a given distance (the radius) from a given point (the center).

8.5 Volume and Surface Area VOLUME OF A SPHERE Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 8.5 Volume and Surface Area c Given the radius, find the volume of a sphere. 6Bowling Ball Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The radius of a standard-sized bowling ball is in. Find the volume of a standard-sized bowling ball. Round to the nearest hundredth of a cubic inch. Use 3.14 for

8.5 Volume and Surface Area d Given the radius and the height, find the volume of a circular cone. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Consider a circle in a plane and choose any point P not in the plane. The circular region, together with the set of all segments connecting P to a point on the circle, is called a circular cone.

8.5 Volume and Surface Area VOLUME OF A CIRCULAR CONE Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of a circular cone with base radius r is one- third the product of the area of the base and the height:

EXAMPLE 8.5 Volume and Surface Area d Given the radius and the height, find the volume of a circular cone. 7 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 8.5 Volume and Surface Area e Solve applied problems involving volumes of rectangular solids, circular cylinders, spheres, and cones. 8Propane Gas Tank Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A propane gas tank is shaped like a circular cylinder with half of a sphere at each end. Find the volume of the tank if the cylindrical section is 5 ft long with a 4-ft diameter. Use 3.14 for

EXAMPLE 8.5 Volume and Surface Area e Solve applied problems involving volumes of rectangular solids, circular cylinders, spheres, and cones. 8Propane Gas Tank Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We first make a drawing.

EXAMPLE 8.5 Volume and Surface Area e Solve applied problems involving volumes of rectangular solids, circular cylinders, spheres, and cones. 8Propane Gas Tank Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate. This is a two-step problem. We first find the volume of the cylindrical portion. Then we find the volume of the two ends and add. Note that together the two ends make a sphere with a radius of 2 ft. We let

EXAMPLE 8.5 Volume and Surface Area e Solve applied problems involving volumes of rectangular solids, circular cylinders, spheres, and cones. 8Propane Gas Tank Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 8.5 Volume and Surface Area e Solve applied problems involving volumes of rectangular solids, circular cylinders, spheres, and cones. 8Propane Gas Tank Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve. The volume of the cylinder is approximately The volume of the two ends is approximately The total volume is about

EXAMPLE 8.5 Volume and Surface Area e Solve applied problems involving volumes of rectangular solids, circular cylinders, spheres, and cones. 8Propane Gas Tank Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. We can repeat the calculations. The answer checks. 5. State. The volume of the tank is about 96.3 ft 3.