Name:
Period:
Foundations of Technology
Unit 2 Lesson 5: Prototypes and Modeling
File 2.5.3: Calculating Surface Area and Volume Review
Date:
Calculating Surface Area and Volume Review
Directions: Use the appropriate equation to answer the following questions. All answers
should be recorded below or in your engineering design journal. Remember to show all
work.
1. Find the areas of the following:
(a). A square with a width and height equal to 5 feet.
(b). A rectangle with a length equal to 8.5 cm and height
equal to 6.0 cm.
(c).A right triangle with a base equal to 24 in and height equal to 18 in.
(d). A circle with a radius equal to 12 feet.
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
2. Find the surface area and volume of a storage cube
measuring 5 feet on each side.
3. Find the surface area and volume of rectangular
prism with a length equal to 15 cm, width equal to
6 cm and a height equal to 7.5 cm.
4. Find the surface area and volume of a basketball with a radius
equal to 29.5 inches. If this basketball was filled with water,
how much water is needed?
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
5. Find the surface area and volume of a cylinder with a
diameter equal to 14 cm and a height equal to 10 cm.
6. The ABC box company makes square puzzle cubes that measure 4 inches along each
edge. They shipped the cubes in a box 8 in x 12 in x 16 in. How many cubes can they
ship in the box?
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
Name:
Period:
Foundations of Technology
Unit 2 Lesson 5: Prototypes and Modeling
File 2.5.3: Calculating Surface Area and Volume Review - ANSWERS
Date:
Calculating Surface Area and Volume Review
Directions: Use the appropriate equation to answer the following questions. All answers
should be recorded below or in your engineering design journal. Remember to show all
work.
1. Find the areas of the following:
(a). A square with a width and height equal to 5 feet.
Equation for Area (A) = a²
A = (5ft)²
A = 25ft²
(b). A rectangle with a length equal to 8.5 cm and height
equal to 6.0 cm.
Equation for Area (A) = W x H
A = 8.5cm x 6cm
A = 51cm²
(c).A right triangle with a base equal to 24 in and height equal to 18 in.
Equation for Area (A) = ½(b x h)
A = ½(24in x 18in)
A = ½(432in²)
A = 216in²
(d). A circle with a radius equal to 12 feet.
Equation for Area (A) = π(r²)
A = π(12ft)²
A = π(144ft²)
A = 452ft²
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
2. Find the surface area and volume of a storage cube
measuring 5 feet on each side.
Equation for Surface Area (SA) = 6a²
SA = 6(5ft)²
SA = 6(25ft²)
SA = 150ft²
Equation Volume (V) = a³
V = (5ft)³
V = 125ft³
3. Find the surface area and volume of rectangular
prism with a length equal to 15 cm, width equal to
6 cm and a height equal to 7.5 cm.
Equation Surface Area (SA) =
2(L x W) + 2(H x W) + 2(L x H)
SA = 2(15cm x 6cm) + 2(7.5cm x 6cm) + 2(15cm x 7.5cm)
SA = 2(90cm²) + 2(45cm²) + 2(112.5cm²)
SA = 180cm² + 90cm² + 225cm²
SA = 495cm²
Equation Volume (V) W x H x D
V = 15cm x 6cm x 7.5 cm
V = 675cm³
4. Find the surface area and volume of a basketball with a radius
equal to 29.5 inches. If this basketball was filled with water,
how much water is needed?
Equation Surface Area (SA) = 4π(r²)
SA = 4π(29.5in)²
SA = 4π(870.25in²)
SA = 10,935in²
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
Equation Volume (V) = 4/3π(r³)
V = 4/3π(29.5in)³
V = 4/3π(25,672in³)
V = 107,536in³
5. Find the surface area and volume of a cylinder with a
diameter equal to 14 cm and a height equal to 10 cm.
Equation Surface Area (SA) =
2π(r²) + 2π(r x h)
SA = 2π(7cm)² + 2π(7cm x 10cm)
SA = 2π(49cm²) + 2π(70cm²)
SA = 308cm² + 440cm²
SA = 748cm²
Equation Volume(V) = π(r²)h
V = π(7cm)²(10cm)
V = π(49cm²)(10cm)
V = 1,539cm³
6. The ABC box company makes square puzzle cubes that measure 4 inches along each
edge. They shipped the cubes in a box 8 in x 12 in x 16 in. How many cubes can they
ship in the box?
Equation Volume (V) of a Cube = a³
Rubics Cube V = 4in³
Rubics Cube V = 64in³
Equation Volume (V) of a Rectangular Prism = W x H x D
Box V = 8in x 12in x 16in
Box V = 1,536in³
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
# of boxes = box volume =
cube volume
1,536in³
64in³
= 24 cubes per box
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
The text passage contains a series of mathematical questions related to calculating surface area and volume, followed by a section with the answers to these questions.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Name:
Period:
Foundations of Technology
Unit 2 Lesson 5: Prototypes and Modeling
File 2.5.3: Calculating Surface Area and Volume Review
Date:
Calculating Surface Area and Volume Review
Directions: Use the appropriate equation to answer the following questions. All answers
should be recorded below or in your engineering design journal. Remember to show all
work.
1. Find the areas of the following:
(a). A square with a width and height equal to 5 feet.
(b). A rectangle with a length equal to 8.5 cm and height
equal to 6.0 cm.
(c).A right triangle with a base equal to 24 in and height equal to 18 in.
(d). A circle with a radius equal to 12 feet.
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
2. Find the surface area and volume of a storage cube
measuring 5 feet on each side.
3. Find the surface area and volume of rectangular
prism with a length equal to 15 cm, width equal to
6 cm and a height equal to 7.5 cm.
4. Find the surface area and volume of a basketball with a radius
equal to 29.5 inches. If this basketball was filled with water,
how much water is needed?
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
5. Find the surface area and volume of a cylinder with a
diameter equal to 14 cm and a height equal to 10 cm.
6. The ABC box company makes square puzzle cubes that measure 4 inches along each
edge. They shipped the cubes in a box 8 in x 12 in x 16 in. How many cubes can they
ship in the box?
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
Name:
Period:
Foundations of Technology
Unit 2 Lesson 5: Prototypes and Modeling
File 2.5.3: Calculating Surface Area and Volume Review - ANSWERS
Date:
Calculating Surface Area and Volume Review
Directions: Use the appropriate equation to answer the following questions. All answers
should be recorded below or in your engineering design journal. Remember to show all
work.
1. Find the areas of the following:
(a). A square with a width and height equal to 5 feet.
Equation for Area (A) = a²
A = (5ft)²
A = 25ft²
(b). A rectangle with a length equal to 8.5 cm and height
equal to 6.0 cm.
Equation for Area (A) = W x H
A = 8.5cm x 6cm
A = 51cm²
(c).A right triangle with a base equal to 24 in and height equal to 18 in.
Equation for Area (A) = ½(b x h)
A = ½(24in x 18in)
A = ½(432in²)
A = 216in²
(d). A circle with a radius equal to 12 feet.
Equation for Area (A) = π(r²)
A = π(12ft)²
A = π(144ft²)
A = 452ft²
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
2. Find the surface area and volume of a storage cube
measuring 5 feet on each side.
Equation for Surface Area (SA) = 6a²
SA = 6(5ft)²
SA = 6(25ft²)
SA = 150ft²
Equation Volume (V) = a³
V = (5ft)³
V = 125ft³
3. Find the surface area and volume of rectangular
prism with a length equal to 15 cm, width equal to
6 cm and a height equal to 7.5 cm.
Equation Surface Area (SA) =
2(L x W) + 2(H x W) + 2(L x H)
SA = 2(15cm x 6cm) + 2(7.5cm x 6cm) + 2(15cm x 7.5cm)
SA = 2(90cm²) + 2(45cm²) + 2(112.5cm²)
SA = 180cm² + 90cm² + 225cm²
SA = 495cm²
Equation Volume (V) W x H x D
V = 15cm x 6cm x 7.5 cm
V = 675cm³
4. Find the surface area and volume of a basketball with a radius
equal to 29.5 inches. If this basketball was filled with water,
how much water is needed?
Equation Surface Area (SA) = 4π(r²)
SA = 4π(29.5in)²
SA = 4π(870.25in²)
SA = 10,935in²
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
Equation Volume (V) = 4/3π(r³)
V = 4/3π(29.5in)³
V = 4/3π(25,672in³)
V = 107,536in³
5. Find the surface area and volume of a cylinder with a
diameter equal to 14 cm and a height equal to 10 cm.
Equation Surface Area (SA) =
2π(r²) + 2π(r x h)
SA = 2π(7cm)² + 2π(7cm x 10cm)
SA = 2π(49cm²) + 2π(70cm²)
SA = 308cm² + 440cm²
SA = 748cm²
Equation Volume(V) = π(r²)h
V = π(7cm)²(10cm)
V = π(49cm²)(10cm)
V = 1,539cm³
6. The ABC box company makes square puzzle cubes that measure 4 inches along each
edge. They shipped the cubes in a box 8 in x 12 in x 16 in. How many cubes can they
ship in the box?
Equation Volume (V) of a Cube = a³
Rubics Cube V = 4in³
Rubics Cube V = 64in³
Equation Volume (V) of a Rectangular Prism = W x H x D
Box V = 8in x 12in x 16in
Box V = 1,536in³
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
# of boxes = box volume =
cube volume
1,536in³
64in³
= 24 cubes per box
©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition /
Technology, Engineering, and Design
user
The text passage contains a series of mathematical questions related to calculating surface area and volume, followed by a section with the answers to these questions.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS