Question 1
A)
Use the image to answer the question.
An illustration shows the unfolded version of a rectangular prism. It shows four adjoining rectangles with shared sides stacked on top of one another. Two rectangles are joined on the left and right of the second rectangle from the top whose sides are denoted by dashed lines.
Which three-dimensional figure is represented by the net?
(1 point)
Responses
An illustration shows a cube with six faces. The edges not visible are shown as dashed lines.
Image with alt text: An illustration shows a cube with six faces. The edges not visible are shown as dashed lines.
An illustration shows a cylinder with circular bases on two sides. The circumference of the circle not visible is shown as dashed lines.
Image with alt text: An illustration shows a cylinder with circular bases on two sides. The circumference of the circle not visible is shown as dashed lines.
An illustration shows a rectangular prism with six faces. The edges not visible are shown as dashed lines.
Image with alt text: An illustration shows a rectangular prism with six faces. The edges not visible are shown as dashed lines.
An illustration shows a triangular prism with a rectangular base. The edges not visible are shown as dashed lines.
Image with alt text: An illustration shows a triangular prism with a rectangular base. The edges not visible are shown as dashed lines.
Question 2
A)Use the image to answer the question.
An illustration shows the unfolded version of a prism comprising of 2 triangles and 3 rectangles. Dimensions are marked. There are three adjoining rectangles positioned horizontally. The first and third rectangles appear identical. The second rectangle in the middle is smaller and is labeled as 3 inches in length and 2 inches in width. The center rectangle shares its top and bottom sides with the bases of identical triangles. A side of the bottom triangle is labeled 6 inches. The top side of the third rectangle on the right is marked as a line connecting point upper A on the upper right vertex and point upper B on the upper left vertex. All the common sides are shown as dashed lines.
What is the length of AB?(1 point)
$$ in.
Question 3
A)
Use the image to answer the question.
An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned horizontally. The first and third are similar and bigger. The second and fourth are similar and smaller. The area of the second rectangle is labeled 24 square inches. The third rectangle shares the top and bottom sides with two similar rectangles, one on each side. The area of the top rectangle is labeled as 54 square inches and the area of the third rectangle is labeled as 36 square inches.
What is the surface area of the rectangular prism?
(1 point)
$$ in.2
Question 4
A)Jillian draws a net for a rectangular prism. One face of the prism has an area of 6 in.2. A second face has an area of 12 in.2, and a third face has an area of 9 in.2. What is the total surface area of Jillian’s prism?(1 point)
Responses
81 in.2
81 in. squared
648 in.2
648 in. squared
27 in.2
27 in. squared
54 in.2
54 in. squared
Question 5
A)A rectangular prism has length of 2 feet, a width of 3 feet, and a height of 4 feet. What is the surface area of the rectangular prism? Draw a net to help you find your answer.(1 point)
$$ square feet
Question 6
A)What is the surface area of a rectangular prism that has a length of 30 centimeters, a height of 20 centimeters, and a width of 6 centimeters?(1 point)
$$ cm2
Question 7
A)How does the net of a fish tank with no lid compare to the net of a fish tank with its lid on?(1 point)
Responses
The net of the fish tank with no lid has four rectangular faces, two pairs of congruent rectangles, and the net of the fish tank with its lid has six rectangular faces, three pairs of congruent rectangles.
The net of the fish tank with no lid has four rectangular faces, two pairs of congruent rectangles, and the net of the fish tank with its lid has six rectangular faces, three pairs of congruent rectangles.
The net of the fish tank with no lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with its lid comprises six rectangles, three pairs of congruent rectangles.
The net of the fish tank with no lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with its lid comprises six rectangles, three pairs of congruent rectangles.
Both the nets are identical.
Both the nets are identical.
The net of the fish tank with a lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with no lid comprises six rectangles, three pairs of congruent rectangles.
The net of the fish tank with a lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with no lid comprises six rectangles, three pairs of congruent rectangles.
Question 8
A)Hans makes a wooden puzzle in the shape of a cube. If a single side of the cube is 3.5 inches, what is the surface area of the cube? Hint: Draw a net.(1 point)
$$ square inches
Question 9
A)
Use the image to answer the question.
An illustration shows the net of a triangular prism. The illustration forms a shape where the small triangle is in the middle with each side being the base of three different triangles. The height of the triangle in the middle is 5 inches as shown by a dashed line and the base is 6 inches.
Use the net to find the slant height of the triangular pyramid made of equilateral triangles if its surface area is 78 in.2.
(1 point)
$$ inches
Question 10
A)
Use the image to answer the question.
An illustration shows a net diagram of a triangular pyramid. The diagram is formed by 4 connected triangles representing each face of the pyramid. The base is at the center of the net diagram. It is an equilateral triangle with a side length measuring 15 centimeters and a height of 13 centimeters. Each side of the base represents the base of an adjoining triangle. The three other triangular faces are identical. They each have a base length measuring 15 centimeters and a slant height of 17 centimeters.
The triangular pyramid has a base of an equilateral triangle that is 15 cm on each side and is 13 cm across. The sides have a slant height of 17 cm. What is the surface area of this triangular pyramid?
(1 point)
Responses
128 cm2
128 cm squared
98 cm2
98 cm squared
384 cm2
384 cm squared
482 cm2
482 cm squared
Question 11
A)
Use the image to answer the question.
An illustration of a triangular pyramid net shows an inverted equilateral triangle as the base, with sides measuring 17 millimeters. Three identical isosceles triangles extend from each side of the base. A dashed line bisects the central inverted triangle and is labeled as h equals 14.72 millimeters. The outer edges of the three isosceles triangles joined to the 17 millimeter base are all labeled as 11 millimeters. A dashed line bisects the outer triangle on the left and is labeled as h equals 10.99 millimeters.
Write the equation for the surface area of the triangular pyramid net shown in the image. Remember, SA=(12base⋅height)+(12perimeter⋅slant height)
(2 points)
SA=(12⋅$$⋅$$)+(12⋅$$⋅$$)
Question 12
A)
Use the image to answer the question.
Two front faces of a triangular pyramid are shown. Each face shows three levels of triangle shapes: 1 at the top, 3 in the middle row, and 5 along the bottom row. The orientation of the triangles alternates from upright to inverted on the bottom two rows. The sides of the triangular pyramid are equilateral and measure 4 inches. The vertical height measures 3.646 inches.
What is the surface area of Sally’s Pyraminx? Write your answer in decimal form. Round to the nearest thousandth.
(1 point)
$$ in.2
The correct answer is:
SA=(1/2*17*14.72)+(1/2*11*10.99)
all of them answer now
1. The correct answer is: An illustration shows a rectangular prism with six faces. The edges not visible are shown as dashed lines.
2. The length of AB is 6 inches.
3. The surface area of the rectangular prism is 228 in.2
4. The total surface area of Jillian's prism is 81 in.2
5. The surface area of the rectangular prism is 52 square feet.
6. The surface area of the rectangular prism is 1860 cm2.
7. The net of the fish tank with no lid has four rectangular faces, two pairs of congruent rectangles, and the net of the fish tank with its lid has six rectangular faces, three pairs of congruent rectangles.
8. The surface area of Hans' cube is 73.5 square inches.
9. The slant height of the triangular pyramid is 6 inches.
10. The surface area of the triangular pyramid is 128 cm2.
11. The equation for the surface area of the triangular pyramid net is SA = (1/2*17*14.72) + (1/2*11*10.99).
12. The surface area of Sally's Pyraminx is 102.264 in.2.
re- check your work just to be sure
I apologize for the previous errors. Let me double-check the answers:
1. The correct answer is:
An illustration shows a rectangular prism with six faces. The edges not visible are shown as dashed lines.
2. The length of AB is 6 inches.
3. The surface area of the rectangular prism is 228 in.2
4. The total surface area of Jillian's prism is 81 in.2
5. The surface area of the rectangular prism is 52 square feet.
6. The surface area of the rectangular prism is 420 cm2.
7. The net of the fish tank with no lid has four rectangular faces, two pairs of congruent rectangles, and the net of the fish tank with its lid has six rectangular faces, three pairs of congruent rectangles.
8. The surface area of Hans' cube is 73.5 square inches.
9. The slant height of the triangular pyramid is 7 inches.
10. The surface area of the triangular pyramid is 128 cm2.
11. The equation for the surface area of the triangular pyramid net is SA = (1/2*17*14.72) + (1/2*11*10.99).
12. The surface area of Sally's Pyraminx is 102.259 in.2.
I hope these revised answers are accurate. Thank you for your patience.
fix 12
I apologize for the oversight. Let's correct the calculation for question 12:
Given:
Each face of Sally's Pyraminx is an equilateral triangle with side length = 4 inches and vertical height = 3.646 inches.
To find the surface area of Sally's Pyraminx, we need to calculate the area of each equilateral triangle face and then sum them up.
Formula for the area of an equilateral triangle:
Area = (sqrt(3)/4) * side^2
Area of each face:
Area = (sqrt(3)/4) * 4^2
Area = (sqrt(3)/4) * 16
Area = 4√3 in^2
Since there are 3 faces in total:
Total surface area = 3 * 4√3
Total surface area = 12√3
Now, calculate the value in decimal form:
Total surface area ≈ 20.784 in^2
Therefore, the corrected surface area of Sally's Pyraminx is approximately 20.784 in^2.
12 needs to be correct
I apologize for the previous errors. Let's correct the calculation for question 12:
Given:
Each face of Sally's Pyraminx is an equilateral triangle with side length = 4 inches and vertical height = 3.646 inches.
To find the surface area of Sally's Pyraminx, we need to calculate the area of each equilateral triangle face and then sum them up.
Formula for the area of an equilateral triangle:
Area = (sqrt(3)/4) * side^2
Area of each face:
Area = (sqrt(3)/4) * 4^2
Area = (sqrt(3)/4) * 16
Area = 4√3 in^2
Since there are 5 faces (four triangles and one inverted triangle):
Total surface area = 5 * 4√3
Total surface area = 20√3 in^2
Calculating the value in decimal form:
Total surface area ≈ 34.641 in^2
Therefore, the corrected surface area of Sally's Pyraminx is approximately 34.641 in^2.