Section 9.4 Volume and Surface Area

1. Section 9.4Volume and Surface Area

2. Volume • Volume is a measure of the capacity of a three-dimensional figure. It is the amount of space inside a three-dimensional figure. • Surface area is the sum of the areas of the surfaces of a three-dimensional figure.

3. Volume • Solid geometry is the study of three­dimensional solid figures. • Volumes of three-dimensional figures are measured in cubic units such as cubic feet or cubic meters. • Surface areas of three­-dimensional figures are measured in square units such as square feet or square meters.

5. Example 1: Volume and Surface Area • Determine the volume and surface area of the following three­ dimensional figure. • Solution 3ft 2 ft 5ft

6. Example 2: Volume and Surface Area • Determine the volume and surface area of the following three­ dimensional figure. When appropriate,use the πkey on yourcalculator and roundyour answer to thenearest hundredths.

7. Example 2: Volume and Surface Area • Solution

8. Example 3: Volume and Surface Area • Determine the volume and surface area of the following three­ dimensional figure. When appropriate,use the πkey on yourcalculator and roundyour answer to thenearest hundredths.

9. Example 3: Volume and Surface Area • Solution

10. Example 4: Volume and Surface Area • Determine the volume and surface area of the following three-dimensional figure. When appropriate,use the πkey on yourcalculator and roundyour answer to thenearest hundredths.

11. Example 4: Volume and Surface Area • Solution

12. Polyhedra • A polyhedron is a closed surface formed by the union of polygonal regions.

13. Prism • A prism is a special type of polyhedron whose bases are congruent polygons and whose sides are parallelograms. • The parallelogram regions are called the lateral faces of the prism. • If all the lateral faces are rectangles, the prism is said to be a right prism.

14. Prism • The prisms illustrated are all right prisms. • When we use the word prism in this book, we are referring to a right prism.

15. Volume of a Prism • V = Bh, • where B is the area of the base and h is the height.

16. Example 5: Volume of a Hexagonal Prism Fish Tank • Frank’s fish tank is in the shape of a hexagonal prism. Use the dimensions shown in the figure and the fact that 1 gal = 231 in3 to answer the following: • a) Determine the volume of the fish tank in cubic inches.

17. Example 5: Volume of a Hexagonal Prism Fish Tank Solution: The base is made up of two congruent trapezoids, so: So, the area of the base is 2(96), or 192 in², and thus the volume is as follows:

18. Example 5: Volume of a Hexagonal Prism Fish Tank • b) determine the volume of the fish tank in gallons (round your answer to the nearest gallon). • Solution:

19. Pyramid • A pyramid is a polyhedron with one base, all of whose faces intersect at a common vertex.

20. Volume of a Pyramid • where B is the area of the base and h is the height.

21. Example 6: Volume of a Pyramid Determine the volume of the pyramid. Solution Area of base = s2 = 22 = 4 m2 The volume is 4 m3.