Asked by A<3
A) Consider the following shapes and determine the horizontal and vertical cross-sections.
(1 point)
B) (1 point)
The horizontal cross-section of this cylinder is a and the vertical cross-section of this cylinder is a
.
Question 2
Area of the Left Side = square centimeters
Area of the Back = square centimeters
A)
7th Grade Math Formula Sheet
Consider the three-dimensional below.
Determine the total surface area of the figure.
(4 points)
Area of the Bottom = square centimeters
TOTAL surface area of the figure = square centimeters
Question 3
Area of each triangular face = square centimeters
Area of the smallest rectangular face = square centimeters
A)
7th Grade Math Formula Sheet
Consider the figure below.
Determine the total surface area of the triangular prism.
(5 points)
Area of the middle rectangular face = square centimeters
Area of the largest rectangular face = square centimeters
TOTAL Surface Area of the Triangular Prism = square centimeters
Question 4
Area of each triangular face = square centimeters
Area of the smallest rectangular face = square centimeters
A)
7th Grade Math Formula Sheet
Consider the following figure.
Determine the total surface area of the triangular prism. Do not round the answers.
(5 points)
Area of the middle rectangular face = square centimeters
Area of the largest rectangular face = square centimeters
TOTAL Surface Area of the Triangular Prism = square centimeters
Question 5
A)
7th Grade Math Formula Sheet
Simone has a red cylindrical storage box that she would like to decorate with patterned paper. How much
paper will Simone need to cover the entire box? Use 3.14 for π. The formula chart is at the bottom of the
page.
Determine the total surface area of the shape. Remember to not round the answers.
(7 points)
Radius of circle = inches Area of each Circular Face = square inches
Total Area of the Circular Faces = square inches
Circumference of Circle = inches Height of Cylinder = inches
Area of the Lateral Face = square inches
Total Surface Area of Cylinder = square inches
Question 6
A)
7th Grade Math Formula Sheet
Consider these two cylinders.
A student says the two cylinders have the same surface area. The surface area of Cylinder
B is 251.2 square inches. Complete the following steps to determine if the student is
correct.
Remember to use 3.14 for π. Do not round the answer.
Radius of Cylinder A = inches Area of Each Circular Face of Cylinder A = square inches
Total Area of the Circular Faces of Cylinder A = square inches
Circumference of Cylinder A = inches Height of Cylinder A = inches
Area of the Lateral Face of Cylinder A = square inches
Total Surface Area of Cylinder A = square inches
(7 points)
B) (1 point)
The surface area of Cylinder A the surface area of Cylinder B.
All Answers 1
Answered by
GPT-5 mini
AI
I can help, but I don’t have the figures or the numeric dimensions — the problems you pasted have blanks where the numbers and pictures should be. Please either upload the images or paste the missing dimensions for each question. Below I list what I need for each problem and give the formulas and step-by-step templates you can use; if you provide the numbers (or the pictures) I’ll fill everything in.
General formulas you’ll need
- Area of a circle: A = πr^2
- Circumference of a circle: C = 2πr
- Lateral surface area of a cylinder: A_lateral = 2πr h
- Total surface area of a cylinder: A_total = 2πr^2 + 2πr h
- Area of a triangle: A = (1/2) × base × height
- Area of a rectangle: A = width × height
- Total surface area of a triangular prism = 2 × (area of triangular base) + sum of areas of the three rectangular faces (each rectangle = side of triangle × prism length)
Question-by-question: what I need and how to compute
Question A (cross-sections)
- If this question concerns a cylinder:
- Horizontal cross-section (plane parallel to the base) → a circle.
- Vertical cross-section (a plane through the axis) → a rectangle (height × diameter) if the plane passes through the axis; if the plane is vertical but not through the axis the cross-section is a rectangle whose height is the cylinder’s height and whose width is a chord length (but typical answer: rectangle of height h and width 2r).
- If the shape is a cone, sphere, rectangular prism, etc., tell me which shape(s) or upload the image and I’ll name the horizontal and vertical cross-sections.
Question 2 (composite 3-D figure total surface area)
What I need:
- The dimensions of the Bottom, Left Side, Back, and any other visible faces (length, width, height).
How to compute:
- Find area of each visible face (rectangles, triangles, circles as appropriate).
- Total surface area = sum of areas of all faces (include any faces not visible if they are part of the exterior).
Example template:
- Area of Left Side = (height × depth) square cm
- Area of Back = (width × height) square cm
- Area of Bottom = (width × depth) square cm
- TOTAL = sum of those areas + any other faces
Question 3 (triangular prism)
What I need:
- Triangle base and height (for area of triangular faces), and prism length (depth).
- The three side lengths of the triangular base (so you can compute the three rectangular face areas: side × prism length).
How to compute:
- Area of each triangular face = (1/2 × triangle base × triangle height)
- Area of smallest rectangular face = (smallest triangle side) × prism length
- Area of middle rectangular face = (middle triangle side) × prism length
- Area of largest rectangular face = (largest triangle side) × prism length
- TOTAL Surface Area = 2 × (area of triangle) + sum of three rectangular areas
Question 4 (another triangular prism)
Same requirements and procedure as Question 3. Provide the triangle side lengths, triangle height (or area), and prism length.
Question 5 (cylindrical storage box)
What I need:
- Radius (r) of the circular faces (you listed “Radius of circle = ___ inches” — give that number).
- Height (h) of the cylinder.
Compute:
- Area of each circular face = π r^2
- Total area of two circular faces = 2 × π r^2
- Circumference = 2 π r
- Area of lateral face = circumference × height = 2π r h
- Total surface area = 2π r^2 + 2π r h
(Use π = 3.14 if requested.)
Question 6 (compare two cylinders)
What I need:
- Radius and height of Cylinder A (you left blanks) and Cylinder B’s surface area you gave as 251.2 in^2.
How to compute Cylinder A surface area:
- Area of each circle = π r_A^2
- Total circular area = 2π r_A^2
- Circumference = 2π r_A
- Lateral area = 2π r_A h_A
- Total surface area_A = 2π r_A^2 + 2π r_A h_A
Then compare SA_A to 251.2. Fill in the comparative statement:
- “The surface area of Cylinder A is (less than / equal to / greater than) the surface area of Cylinder B.”
If you upload the pictures or give me the missing numerical values (for every blank), I will compute each requested area and fill in every blank step-by-step, using π = 3.14 if you want. Which questions/dimensions would you like me to solve first?
General formulas you’ll need
- Area of a circle: A = πr^2
- Circumference of a circle: C = 2πr
- Lateral surface area of a cylinder: A_lateral = 2πr h
- Total surface area of a cylinder: A_total = 2πr^2 + 2πr h
- Area of a triangle: A = (1/2) × base × height
- Area of a rectangle: A = width × height
- Total surface area of a triangular prism = 2 × (area of triangular base) + sum of areas of the three rectangular faces (each rectangle = side of triangle × prism length)
Question-by-question: what I need and how to compute
Question A (cross-sections)
- If this question concerns a cylinder:
- Horizontal cross-section (plane parallel to the base) → a circle.
- Vertical cross-section (a plane through the axis) → a rectangle (height × diameter) if the plane passes through the axis; if the plane is vertical but not through the axis the cross-section is a rectangle whose height is the cylinder’s height and whose width is a chord length (but typical answer: rectangle of height h and width 2r).
- If the shape is a cone, sphere, rectangular prism, etc., tell me which shape(s) or upload the image and I’ll name the horizontal and vertical cross-sections.
Question 2 (composite 3-D figure total surface area)
What I need:
- The dimensions of the Bottom, Left Side, Back, and any other visible faces (length, width, height).
How to compute:
- Find area of each visible face (rectangles, triangles, circles as appropriate).
- Total surface area = sum of areas of all faces (include any faces not visible if they are part of the exterior).
Example template:
- Area of Left Side = (height × depth) square cm
- Area of Back = (width × height) square cm
- Area of Bottom = (width × depth) square cm
- TOTAL = sum of those areas + any other faces
Question 3 (triangular prism)
What I need:
- Triangle base and height (for area of triangular faces), and prism length (depth).
- The three side lengths of the triangular base (so you can compute the three rectangular face areas: side × prism length).
How to compute:
- Area of each triangular face = (1/2 × triangle base × triangle height)
- Area of smallest rectangular face = (smallest triangle side) × prism length
- Area of middle rectangular face = (middle triangle side) × prism length
- Area of largest rectangular face = (largest triangle side) × prism length
- TOTAL Surface Area = 2 × (area of triangle) + sum of three rectangular areas
Question 4 (another triangular prism)
Same requirements and procedure as Question 3. Provide the triangle side lengths, triangle height (or area), and prism length.
Question 5 (cylindrical storage box)
What I need:
- Radius (r) of the circular faces (you listed “Radius of circle = ___ inches” — give that number).
- Height (h) of the cylinder.
Compute:
- Area of each circular face = π r^2
- Total area of two circular faces = 2 × π r^2
- Circumference = 2 π r
- Area of lateral face = circumference × height = 2π r h
- Total surface area = 2π r^2 + 2π r h
(Use π = 3.14 if requested.)
Question 6 (compare two cylinders)
What I need:
- Radius and height of Cylinder A (you left blanks) and Cylinder B’s surface area you gave as 251.2 in^2.
How to compute Cylinder A surface area:
- Area of each circle = π r_A^2
- Total circular area = 2π r_A^2
- Circumference = 2π r_A
- Lateral area = 2π r_A h_A
- Total surface area_A = 2π r_A^2 + 2π r_A h_A
Then compare SA_A to 251.2. Fill in the comparative statement:
- “The surface area of Cylinder A is (less than / equal to / greater than) the surface area of Cylinder B.”
If you upload the pictures or give me the missing numerical values (for every blank), I will compute each requested area and fill in every blank step-by-step, using π = 3.14 if you want. Which questions/dimensions would you like me to solve first?
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