1. A prism is a solid whose sides (lateral sides) are parallelograms and whose bases are a pair of identical parallel polygons. A polygon is a simple closed figure whose sides are line segments. Bases Rectangular prismPentagonal prism Triangular prism

2. The volume of a solid is the number of cubes it takes to fill the solid. The volume of a prism is found by multiplying the area of the base (B) by the height of the prism. The height is the distance between the 2 bases.

3. Find the volume of a rectangular prism that has length of 7cm, with of 6 cm and height of 4 cm. 7 cm 6 cm 4 cm

4. Steel weighs 0.28. What is the weight of a rectangular piece of steel 0.25 in. by 15.0 in. by 32.0 in?

5. A cylinder is a geometric solid with a curved lateral surface. A can is an example of a cylinder. The volume of a cylinder is given by r h

6. Example: Find the volume of the cylinder. d = 24 m 40 m Since d = 24, then r = 12 m.

7. The volume of any cone or pyramid is given by the formula height Base Slant height diameter height Base where B = area of the base Apex

8. Find the volume.

9. 19.6 cm

10. The volume of a sphere is given by the formula

11. The lateral surface area is the sum of the areas of the lateral faces of the prism. LSA = ph, where p is the perimeter of the base and h is the height of the prism.

12. Find the lateral surface area of a rectangular prism that has length of 7cm, with of 6 cm and height of 4 cm. 7 cm 6 cm 4 cm Front and back = 4 x 7 each = 2(28) = 56 sq. cm. 2 ends = 4 x 6 each = 2(24) = 48 sq. cm. Lateral surface area = 104 sq. cm.

13. The total surface area is found by finding the sum of the lateral area faces and the areas of the bases. TSA = ph + 2B 7 cm 6 cm 4 cm Lateral surface area = 104 sq. cm. The top and bottom are the bases. Top area = 6 x 7 = 42 sq. cm. Same for the bottom = 42 sq. cm Area of the bases = 2(42) = 84 sq. cm. Total S.A. = 104 + 84 = 188 sq. cm.

14. The lateral surface area of a cylinder and be visualized by taking a can, cutting out the top and bottom, then down the side and unrolling the can. The resulting shape is a rectangle that has length equal to the circumference of the circular top and width equal to the height of the can. The formula is

15. The total surface area is the sum of the lateral area and the 2 bases (top and bottom)

16. Find the lateral surface area and total surface area of the cylinder. Lat. S.A.= Total S.A.= Lat.S.A. + 2 bases, where the bases are circles 2.5 in 12 in

17. A steel cylindrical tank needs to hold 7000 gal. Due to space constraints, the tank should be 10 ft in diameter. How tall should the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/cu.ft.) First convert gal to cu.ft. Take this volume and radius of 5 ft, substitute them into the volume formula and solve for h.

18. Example continued:

19. Find the amount of paper used for labels for 1000 cans like those shown below. 8.24 cm 3.16 cm Sweetheart Chicken Soup

20. The total surface area of a sphere is given by TSA = 4πr²

21. Lateral surface area of a cone is given by LSA = πrs, where r is the radius and s is the slant height, and the total surface area is given by TSA = πrs + πr²

22. Find the lateral surface area and total surface area of a cone that has a radius of 6 ft, slant height of 10 ft and height of 8 ft.