Geometry of Packaging

Name:……………………………..

For the last week of Math 10 Foundations, we are going to study the measurement of two dimensional and three dimensional (solids). In this project, you will be calculating the perimeter, area, surface area and volume of shapes and solids. You will then use these calculations to determine the amount of covering required to cover the surface area of the different solids, the amount of material to fill a specified solid or the amount of fencing required to fence a lot.

Another way that this type of geometry is used is to calculate the Economy Rate (referred to as ER). Economy Rate is the ratio of Volume to Surface Area.

If this ratio is high, that means the package has more volume than surface area, making it a more economical design. If it is a low number too much material is being used to make the package, making it less economical. ER has led to some interesting discussions in the marketplace and has contributed to the miniaturization of packaging of many products in our stores.

Use the formula sheets to help you calculate the required measurement on the following sheets. Your work should include the original formula, the substitution and the answer with the correct units. Only part marks will be given for answers only. Answers should be expressed to the nearest hundredth with the unit written.

Do your work on scrap paper first then copy your correct work on this assignment. Be neat. Messy presentation will result loss of points.

Your Geometry Unit mark will consist of the completion of this booklet (worth 6%), three comprehension questions (worth 1% each) and a Geometry Section on the Unit test on Monday Jan. 21st(worth 1%).

Item / Due Date
Comp Question 1 / Weds. 16th Jan
Comp Question 2 / Thurs. 17th Jan
Comp Question 3 / Fri. 18th Jan
Geometry Section on Unit Test / Mon. 21st Jan
Booklet / Tues. 22nd Jan


Page 1 – Applications of Volume (16 marks)

Calculate the Volume of each solid correctly to one decimal place.

a. A cube with a side length of 8 cm
/ b. Height is 18cm, Length is 9.5 cm, Width is 6.5 cm

Final Answer: / Final Answer:
c. H= 21 cm, b = 10.5 cm
/ d. Radius is 3 cm and Height is 4.5 cm

Final Answer: / Final Answer:
e.
/ f. Radius is 10 cm
Final Answer: / Final Answer:
g. If one guppy requires 5L of water to live happily, what is the maximum of guppies that should be kept in an aquarium 30cm by 40 cm by 30 cm? (1000 cm3 = 1 Litre)
Final Answer:
h. A truck can carry 7.5 m3 of earth. How many truckloads will be needed to carry away the earth dug from a well 2.2 m in diameter and 32 m deep?
Final Answer:

Section 2: Economy Rate (19 marks)

Calculate the Volume and Total Surface Area of each solid correctly to one decimal place. Calculate the Economy Rate.

a.
/ b.

Volume =
Surface Area=
Economy Rate = / Volume =
Surface Area=
Economy Rate =
c.
/ d. Slant height is 50 mm and radius is 30 mm
Volume =
Surface Area=
Economy Rate = / Volume =
Surface Area=
Economy Rate =
e. Slant Height is 20 m
/ f. Diameter is 10 cm
Volume =
Surface Area=
Economy Rate = / Volume =
Surface Area=
Economy Rate =
g. Which is the least economical shape?
h. Which is the most economical shape?


Section 3: Areas of Shaded Regions (15 marks)

Calculate the Area of the shaded region of each figure to the nearest whole unit. The letter C shows the center of the circle.

a.
/ b. Border is 1 cm wide all the way around
Final Answer: / Final Answer:
c. All units are in metres. / d.

Final Answer: / Final Answer:
e. A display platform is shown. Find the area of carpeting required to completely cover the surface of the platform. If carpet costs $3.50 m2, how much will it cost to carpet this platform?


Final Answer:

Section 4: Surface Area (9 marks Bonus is worth 3 marks)

Calculate the total surface area of each shape. Break the shape into parts and find each individual area. Total the areas to get total surface area.

a. All units are in cm. / b.

Final Answer: / Final Answer:
c.
/ d. BONUS (All units are in m.)

Final Answer: / Final Answer:

Section 5: Real World Applications (15 marks)

Include your diagrams and answer to 1 decimal point.

a.  A tornado is a narrow funnel shaped cloud similar to a cone. The diameter of this tornado is 82 m and its height is 860 m. Calculate the volume of the funnel of the tornado.
Final Answer:
b.  A rectangular field is 18 m long and 7 m wide. Calculate the cost of sodding the field if sod costs $10.75 m2.
Final Answer:
c.  Calculate the area of material needed to produce the sails for this boat.


Final Answer:
d.  Farmer Brown stores grain in a silo that is in the shape of a cylinder. The surface area of this silo is approximately 320 (or 1005) m2 with a radius of 8m. What is the height of the Silo?
Final Answer:
e.  A lime spreader is shaped like a rectangular based prism. It has the following dimensions. The open end is 2.3 m by 4.1 m and the depth is 3.5 m. The bottom (closed) end is 1.8m by 4.1m. If it has a full load how much lime can it hold? If it distributes the lime over the grass at a rate of 0.2 m3/min how long will it take to empty the load?
Final Answer:

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