Fudge Trays
The Fudge Company makes open topped rectangular trays to package fudge. They use cellophane to cover the trays. The material used to make the trays measures 24 centimeters by 20 centimeters. The trays are created by cutting squares of equal size from each corner and folding the remaining portions up to form the sides. The trays for the Fudge Company must have a volume of at least 750 cubic centimeters. In addition, they want to use the surfaces of the tray for advertisements. The surface areas used for advertisement include the four exterior sides and the exterior bottom of the tray. They want to have at least 420 square centimeters available for advertising.
Each group will use centimeter graph paper to construct a few of the trays that are possible. Complete the following tables. If necessary, centimeter cubes can be used to find the volume and surface area.
Length of side of cut out square / Length of tray(cm) / Width of tray
(cm) / Height of tray
(cm) / Process to calculate volume
(cm3) / Volume of tray
(cm3)
1
2
3
4
5
6
7
8
9
Length of side of cut out square / Area of the base / Area of the lateral faces / Total Surface Area
(cm2)
Process
(cm2) / Solution
(cm2) / Process
(cm2) / Solution
(cm2)
1
2
3
4
5
6
7
8
9
Summarize your data in the chart below
Length of side of cut out square / Length of tray(cm) / Width of tray
(cm) / Height of tray
(cm) / Surface area
(cm2) / Volume of tray
(cm3)
1
2
3
4
5
6
7
8
9
10
1. What are the dimensions of the tray with the greatest volume? ______
Support you’re answer with words, numbers and/or diagrams.
2. What are the dimensions of the square that is cut from the corner to make this tray? ______
Support you’re answer with words, numbers and/or diagrams.
3. What are the dimensions of the tray with the greatest surface area for advertising? ______
Support you’re answer with words, numbers and/or diagrams.
4. What are the dimensions of the square that is cut from the corner to make this tray? ______
Support you’re answer with words, numbers and/or diagrams.
5. What are the dimensions of the square that you would cut from the corners to form a tray that
serves both the packaging and the advertising needs? ______
Explain using information from the tables above.
Moving Mount Spokane
The engineers in the I Dig It Company of Spokane designed aconveyor belt that can move 9000 cubic yards of earth per hour. Since this sounds like a great quantity of earth that could be moved in a day, week or month, we were wondering how long it would take to move Mt. Spokane! You have been contracted by the I Dig It Company to calculate the amount of earth in Mt. Spokane and you must determine how long it would take to move Mt. Spokane. You are also to answer some other relative questions dealing with such a gigantic task.
- The city of Spokane is approximately 1880 feet above sea level. The base of Mt. Spokane is approximately 2300 feet above sea level. The top of Mt. Spokane is approximately 5883 feet above sea level. What is the height of Mt. Spokane from its base? Show all calculations.
2. The diameter of the base is 21 miles and the mountain is cone-shaped. You need to convert miles into feet and then into yards to compute the volume of Mt. Spokane. How many feet are there in 1 mile? How many feet are there in 1 yard?
3. Let’s convert the diameter of the base of Mt. Spokane into feet. Complete the following ratio.
4. Now convert the answer to yards.
5. What is the area of the base of Mt. Spokane in square yards?
6.What would be the volume of earth contained in Mt. Spokane in cubic yards? Show and explain ALL of your calculations. The formula for the volume of a cone is , where B is the area of the base of the cone, and h is the height of the cone.
______
______
7.The president of the company was told that the diameter of the base of Mt. Spokane was miscalculated. The actual diameter is half of what was originally told to him. What is the correct diameter of Mt. Spokane? Calculate the new volume of Mt. Spokane.
- Write the ratio of the original volume to new volume. How does this compare to the ratio of the original diameter to the correct diameter? Explain.
Convey Your Cost
9.The conveyor moves 9000 cubic yards per hour. How long would it take to move Mt. Spokane with the conveyor? Show and explain ALL of your calculations. Convert your answer to a meaningful unit of time.
10.The previous edition of the conveyor used by the I Dig It Company moved 5720 cubic yards of earth per hour. In addition to the difference in actual time in moving earth, the new conveyor is also more cost efficient. The older machine cost the company, taking into account all expenses, $64.24 per hour to operate. The new conveyor cost the company $43.54 per hour to operate. How much cheaper is it to move Mt. Spokane with the new conveyor as opposed to the older machine? Show and explain ALL of your calculations.
Moving Mt Spokane – Practice Problems
11. An edge of Cube A is twice as long as an edge of Cube B as shown in the figure below.
Which is the maximum number of smaller cubes that will fit into the interior of the larger cube?
A. 2
B. 4
C. 8
D. 16
12. The Great Pyramid at Giza has a square base with sides of length 230 meters and a height of 146.7 meters.
Which is the volume of the Great Pyramid?
A. 1,650,000 m³
B. 2,590,000 m³
C. 4,950,000 m³
D. 7,760,000 m³
13. The radius of the earth’s orbit is 150,000,000,000 meters.
Which is this number in scientific notation?
A.
B.
C.
D.
14. Which number is equivalent to 3.01 x 10?
A. 0.00000000301
B. 0.0000000301
C. 301,000,000
D. 30,100,000,000
15. A planned building was going to be 100 feet long, 75 feet deep, and 30 feet high. The owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and height.
Which is the new length of this building?
A. 106 feet
B. 108 feet
C. 110 feet
D. 112 feet
16. A circular garden has a diameter of 12 feet. One bag of topsoil covers an area of 3 square feet.
Which is the number of bags needed to cover the garden.
A. 13
B. 16
C. 38
D. 40
17. What is the sum of and ?
A.
B.
C.
D.
1
Student: Ch 18 “Moving Mount Spokane”