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Area, Perimeter, Volume and Pythagorean Theorem
Assessment
Name: _____________________________
1. Find the perimeter of a right triangle with legs measuring 10 inches and 24
inches
a. 34 inches
b. 60 inches
c. 120 inches
d. 240 inches
2. The side lengths of the base of right prism are doubled while the height is not
changed. Which of the following best describes the result on the volume of the
prism
a.
The volume remains the same
b.
The volume doubles
c.
The volume triples
d.
The volume quadruples
3. A square pasture is bordered on one side by a stream and on the other three
sides by a fence. If the fence is 204 feet long, what would be the area of the
pasture?
a.
408 square feet
b.
2,601 square feet
c.
4,624 square feet
d.
10,404 square feet
Designing Boxes
Assessment Page 1 of 13
4. A cylinder has radius of 6 cm and height of 8 cm what would be its volume?
a.
48 cubic cm
b.
96 cubic cm
c.
226 cubic cm
d.
905 cubic cm
5. A cylindrical tank has diameter of 6 m and height of 10 m what would be its
surface area?
a.
60 square m
b.
90 square m
c.
245 square cm
d.
528 square cm
6. If the volume of a new container is 8 times larger than a previous container, by
how much has each dimension increased?
a.
2 times
b.
3 times
c.
4 times
d.
8 times
Designing Boxes
Assessment Page 2 of 13
7. Because of a change in her company’s best selling product, Korie has been given
the job of redesigning the packaging for the latest product upgrade. The marketing
department has told her that the package needs to be larger to catch the customers’
eye on the shelf. She decides to double each edge length. The volume of the old
container was 27 cubic inches.
•
What is the volume of the new package?
Show your work using words, numbers and/or diagrams.
The volume of the new package is __________________ cubic inches.
Designing Boxes
Assessment Page 3 of 13
8. Harold is the marketing manager for a major toy company. His company is ready
to release a new toy. Harold’s research tells him that more people will buy the
toy if the front of the box has a surface area of 54 square inches. The depth of
the box Harold designs is the same as one of the edge lengths of the front of the
box. All of Harold’s measurements are whole numbers (no fractions or
decimals). As always, Harold designs a box that sells well.
•
What is the volume of the box he designs?
Show your work using words, numbers and/or diagrams.
The volume of the new package is __________________ cubic inches.
Designing Boxes
Assessment Page 4 of 13
9. Jerry works for a shipping company whose customer has requested a square
based container with a volume of 96 cubic feet. The dimensions of the container
must be whole number values (no fractions or decimals) per the customer’s
request. As always, Jerry makes his customer happy.
•
What are the dimensions of the container he designs?
Show your work using words, numbers and/or diagrams.
The dimensions of the container are __________________ feet.
Designing Boxes
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10. As the product manager for a packaging company, Chuck is responsible for
creating the package that best fits his customers’ needs. His customer has
decided to change their packaging for the summer season. The current
package holds a pen that reaches diagonally through the center of a cube
measuring 8 inches on an edge. Chuck is given the job of creating a cylindrical
prism container that has equal diameter and height that will hold the same pen.
Chuck also needs to calculate and compare the cost of the package options.
The material used to build the cube cost $0.35 per square inch and the material
for the cylinder costs $0.32 per square inch.
8”
8”
x”
x”
8”
• What is the diameter of the cylinder? (round your answer to two decimal places)
• What is the height of the cylinder? (round your answer to two decimal places)
• Identify the more expensive option and the cost to build it.
• Determine which package costs more to build and state its cost.
Helpful ideas:
Circumference of a circle: C = πd
Area of a circle:
A = πr2
Show your work using words, numbers and/or diagrams.
Designing Boxes
Assessment Page 6 of 13
8”
8”
x”
x”
8”
The diameter and height of the cylinder is __________________ inches.
The __________________ is more expensive to build. It costs ________________
Designing Boxes
Assessment Page 7 of 13
Area, Perimeter, Volume and Pythagorean Theorem
Assessment Solutions
Area, Perimeter, Volume and Pythagorean Theorem Quiz
3. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches
a.
34 inches
b.
60 inches
c.
120 inches
d.
240 inches
4. The side lengths of the base of right prism are doubled while the height is not
changed. Which of the following best describes the result on the volume of the
prism
a.
The volume remains the same
b.
The volume doubles
c.
The volume triples
d.
The volume quadruples
3. A square pasture is bordered on one side by a stream and on the other three
sides by a fence. If the fence is 204 feet long, what would be the area of the
pasture?
a.
408 square feet
b.
2,601 square feet
c.
4,624 square feet
d.
10,404 square feet
4. A cylinder has radius of 6 cm and height of 8 cm what is its volume?
a.
48 cubic cm
b.
96 cubic cm
c.
226 cubic cm
d.
905 cubic cm
5. A cylindrical tank has diameter of 6 m and height of 10 m what is its surface area?
a.
60 square m
b.
90 square m
c.
245 square m
d.
528 square m
6. If the volume of a new container is 8 times larger than a previous container, by
how much has each dimension increased?
a.
2 times
b.
3 times
c.
4 times
d.
8 times
Designing Boxes
Assessment Page 8 of 13
9. Because of a change in her company’s best selling product, Korie has been given
the job of redesigning the packaging for the latest product upgrade. The marketing
department has told her that the package needs to be larger to catch the customers’
eye on the shelf. She decides to double each edge length. The volume of the old
container was 27 cubic inches.
What is the volume of the new package?
Show your work using words, numbers and/or diagrams.
Volume was 27 cubic inches so possible container would be 3X3X3.
If she doubles them then it would be 6X6X6 for a total of 216 cubic inches.
OR
As edge lengths all increase by a factor of 2, the volume increases by 23
So, new volume is 8X27 = 216 cubic inches.
The volume of the new package is ________216______ cubic inches.
Designing Boxes
Assessment Page 9 of 13
10. Harold is the marketing manager for a major toy company. His company is ready to
release a new toy. Harold’s research tells him that more people will buy the toy if
the front of the box has a surface area of 54 cubic inches. The depth of the box
Harold designs is the same as one of the edge lengths of the front of the box. All of
Harold’s measurements are whole numbers (no fractions or decimals). As always,
Harold designs a box that sells well.
What is the surface area of the box he designs?
Show your work using words, numbers and/or diagrams.
Surface area is 54 square inches and two of the dimensions are equal, so I need
a perfect square that divides 54. That number is 9. Thus, the equal edges are 3
inches each and the third is 54 divided by 9 or 6.
So the box is 3X3X6 and its surface area is:
Sides:
3X6X4 = 72 square inches
Top and Bottom: 3X3X2 = 18 square inches
Then the total surface area is 90 square inches
The surface area of the new package is _______90_____ square inches.
Designing Boxes
Assessment Page 10 of 13
11. Jerry works for a shipping company whose customer has requested a square
based container with a volume of 96 cubic feet. The dimensions of the container
must be whole number values (no fractions or decimals) per the customer’s
request. As always, Jerry makes his customer happy.
What are the dimensions of the container he designs?
Show your work using words, numbers and/or diagrams.
I need a perfect square that evenly divides 96.
That number is 16. So two of the dimensions are 4 feet and 4 feet.
Then the third dimension is 96 divided by 16 or 6.
The dimensions of the container are _____4X4X6________ feet.
Designing Boxes
Assessment Page 11 of 13
10.
As the product manager for a packaging company, Chuck is responsible for
creating the package that best fits his customers’ needs. His customer has
decided to change their packaging for the summer season. The current package
holds a pen that reaches diagonally through the center of a cube measuring 8
inches on an edge. Chuck is given the job of creating a cylindrical prism container
that has equal diameter and height that will, hold the same pen. Chuck also needs
to calculate and compare the cost of the package options. The material used to
build the cube cost $0.35 per square inch and the material for the cylinder costs
$0.32 per square inch.
8”
8”
x”
x”
8”
•
What is the diameter of the cylinder? (Round your answer to two decimal
places)
• What is the of the cylinder? (Round your answer to two decimal places)
• Identify the more expensive option and the cost to build it.
Helpful ideas:
Circumference of a circle: C = πd
Area of a circle:
A = πr2
Show work to support your answers using words, numbers and/or diagrams.
Designing Boxes
Assessment Page 12 of 13
8”
8”
8”
x”
x”
First, find diagonal of cube: 8sqrt3 ≅ 13.86
Then in the cylinder the diagonal is 13.86 and since diameter and height are equal, use
Pythagorean Theorem to solve for diameter and height with equal leg lengths
(alternately use 45-45-90 relationship).
Thus we get dimension of cylinder of 9.80 inches diameter and height
Then find S.A. of cube: 64x6 = 384 square inches.
Use formulas on front to find S.A. of cylinder 9.82(π)+ 2(π)4.92 = 452 square inches
Now cost to produce Cube is 384x0.35 = $134.40
Cost to produce Cylinder is 452x0.32 = $144.64
So the cylinder costs more to produce.
The diameter and height of the cylinder is ________9.80________ inches.
The __________cylinder ____ is more expensive to build.
It costs _______$144.64____
Designing Boxes
Assessment Page 13 of 13