| |
For all of the problems in this unit, label answers correctly and round to the nearest tenth, if necessary, unless specified otherwise. |
|
|
| |
| |
|
| |
|
3) An architect designs an A-frame house with the floor measuring 35 feet by 56 feet. The front of the house has the shape of an equilateral triangle with all sides measuring 35 feet and the height measuring 30 feet. Answer the following questions: (a) What is the area of the triangular front of the house? (b) What is the volume of the house? |
|
4000 character(s) left Your answer is too long. |
|
| |
|
| |
|
Refer to the following information to solve the next problem: Cement is sold in cubic yards. A cubic unit (cubic yard) is a unit of volume. A cubic yard is equivalent to the volume of a cube that measures 1 yard, or 3 ft, on each edge. |
|
|
| |
| |
|
| |
6) Which of the numbers below is NOT a perfect cube (a number that is an integer multiplied by itself three times)? Use a scientific calculator to help determine the answer. |
|
|
|
| |
|
7) Use approximation to find the cube root of 450 rounded to the nearest hundredth, and then answer the following questions: (a) The number, 450, falls between what two perfect cubes? (b) What are the cube roots of these two perfect cubes? (c) Between what two decimal numbers, expressed in tenths, does the cube root of 450 fall? (d) To the nearest hundredth, the cube root of 450 is closest to what number? |
|
4000 character(s) left Your answer is too long. |
|
| |
|
| |
|
| |
|
| |
|
Volume of Right Cylinders |
|
|
| |
For all problems that have formulas that include “pi”, use 3.14 for pi. |
|
|
| |
| |
|
| |
|
| |
|
| |
|
| |
|
Volume of Right Cones and Pyramids |
|
|
| |
| |
|
| |
|
| |
|
19) A cone has a slant height of 24 inches and the height and radius are equal in measure. (a) What is the length of the radius of the cone? (b) What is the height of the cone? (c) What is the volume of the cone? |
|
4000 character(s) left Your answer is too long. |
|
| |
|
| |
|
21) The volume of a pyramid is equal to __________ of the volume of a prism with the same base area and height. |
|
|
|
| |
|
| |
|
| |
|
| |
|
| |
|
| |
26) Which of the following BEST describes the application of Cavalieri’s Principle? |
|
|
|
| |
|
| |
|
| |
|
| |
|
| |
| |
|
| |
|
| |
|
33) The surface area of a sphere is 40,000 square feet. (a) What is the radius? (b) What is the volume of the sphere? |
|
4000 character(s) left Your answer is too long. |
|
| |
|
Similar and Congruent Solids |
|
|
| |
34) Which statement BEST describes the pyramids? |
|
|
|
| |
|
35) Which statement BEST describes the pyramids? |
|
|
|
| |
|
36) Which statement BEST describes the spheres? |
|
|
|
| |
|
Refer to the rectangular prisms shown below to solve the next six problems. Through these problems, you will investigate how similarity affects surface areas and volumes of solids. |
|
|
| |
37) What is the scale factor between the lengths, widths, and heights of the two similar prisms? Compare Prism A to Prism B. |
|
|
|
| |
|
| |
|
39) Write a ratio that compares the surface area of Prism A to the surface area of Prism B. What is the SIMPLIFIED scale factor between the surface areas of the two prisms? |
|
|
|
| |
|
| |
|
41) Write a ratio that compares the volume of Prism A to the surface area of Prism B. What is the SIMPLIFIED scale factor between the volumes of the two prisms? |
|
|
|
| |
|
42) Look over the results of the previous problems. Compare the original scale factor, the simplified scale factor of the surface areas, and the simplified scale factor of the volumes. Complete the following statement. It is modeled from Theorem 29 and the results in the previous problems. If two solids are similar, with a scale factor of “a: b”, then the surface areas have a ratio that is the__________ of “a” and the __________ of “b”. The volumes have a ratio that is the __________of “a” and the __________ of “b”. |
|
|
|
|
|
|
|
| |
|
| |
|
Extended Research: Check with your instructor to see if he/she is interested in awarding extra credit to you for writing a one-page report on the following research topic: Research the Internet to find information about “geodesic domes”. In the report include a description of the geometric shape, the kind of structure it is, the history of the development of this type of structure, some pros and cons about the use of this structure, and some examples of where and how structures of this type are currently being used. You may also include pictures. Be sure to include a list of websites that you referenced when writing the report. |
|
|
| |
44) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
|
No offline activities found |
0 Hour(s) & 0 Minute(s)
|
|
|
Attachments |
|