Right Rectangular Prisms & Pyramids Unit Test
2 of 152 of 15 Items
Question
Use the image to answer the question.
An photograph shows multiple pyramids and a desert in the foreground. Three large pyramids appear in the center of the image. Three smaller pyramids are in front of the larger pyramids.
Source: Waj/Shutterstock
Jamie has been assigned to replicate the pyramids of Giza in Egypt. What type of pyramids are these? Describe the attributes.
(1 point)
Responses
They are triangular pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
They are triangular pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
They are square pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
They are square pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
They are square pyramids. They have 4 faces. The 3 lateral faces are triangles, and the 4th face is a square base. Each pyramid has 6 vertices and 8 edges. The 3 lateral faces meet at a single point, or apex.
They are square pyramids. They have 4 faces. The 3 lateral faces are triangles, and the 4th face is a square base. Each pyramid has 6 vertices and 8 edges. The 3 lateral faces meet at a single point, or apex.
They are right rectangular pyramids. They have 6 faces. The 5 lateral faces are triangles, and the 6th face is a triangular base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
They are right rectangular pyramids. They have 6 faces. The 5 lateral faces are triangles, and the 6th face is a triangular base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
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They are triangular pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
What is the surface area of a right rectangular prism where each edge length measures 15.10 cm?(1 point)
Responses
1,368.06 cm2
1,368.06 cm squared
1,350 cm2
1,350 cm squared
8,208.36 cm2
8,208.36 cm squared
900 cm2
900 cm squared
The surface area of a right rectangular prism can be found by using the formula:
Surface Area = 2(ab + bc + ac)
Given that each edge length measures 15.10 cm, we can substitute this value into the formula:
Surface Area = 2(15.10*15.10 + 15.10*15.10 + 15.10*15.10)
Surface Area = 2(228.01 + 228.01 + 228.01)
Surface Area = 2(684.03)
Surface Area = 1368.06 cm²
Therefore, the correct answer is 1,368.06 cm².
Right Rectangular Prisms & Pyramids Unit Test
4 of 154 of 15 Items
Question
Use the image to answer the question.
An illustration shows a Rubik’s cube made up of three by three smaller cubes on each side.
Given that each square is 1 inch, find the surface area of this puzzle game.
(1 point)
Responses
18 in.2
18 in. squared
9 in.2
9 in. squared
54 in.2
54 in. squared
54 cm2
54 cm squared
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The Rubik’s cube consists of 6 faces, each made up of 9 smaller cubes. Since each smaller cube has a length of 1 inch, the surface area of each face is (1 inch * 1 inch) * 9 = 9 square inches.
Therefore, the total surface area of the Rubik’s cube is 6 faces * 9 square inches = 54 square inches.
The correct answer is 54 in.²
Question
A carry-on suitcase is 9.5 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase?(1 point)
Responses
3,420 in.2
3 comma 420 in. squared
725.75 in.2
725 point 7 5 in. squared
1,451.5 in.2
1 comma 451 point 5 in. squared
96 in.2
96 in. squared
To find the surface area of the suitcase, we need to calculate the area of each of its six faces and then sum them up.
The surface area of a rectangular face is given by the formula: Area = length * width.
Given the dimensions of the suitcase:
Length = 9.5 inches
Width = 16 inches
Height = 22.5 inches
Face 1: Area = length * width = 9.5 in * 16 in = 152 in²
Face 2: Area = length * width = 9.5 in * 16 in = 152 in²
Face 3: Area = length * width = 16 in * 22.5 in = 360 in²
Face 4: Area = length * width = 16 in * 22.5 in = 360 in²
Face 5: Area = length * width = 9.5 in * 22.5 in = 213.75 in²
Face 6: Area = length * width = 9.5 in * 22.5 in = 213.75 in²
Summing up the areas of all six faces: 152 in² + 152 in² + 360 in² + 360 in² + 213.75 in² + 213.75 in² = 1451.5 in².
Therefore, the surface area of the suitcase is 1451.5 in².
The correct answer is 1,451.5 in.².
Find the surface area of a rectangular pyramid with these measurements: l = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
m2
To find the surface area of a rectangular pyramid, we need to calculate the area of each of its faces and then sum them up.
Given the dimensions of the rectangular pyramid:
Length (l) = 15 m
Width (w) = 12 m
Height (h) = 10 m
Base Area: Area = length * width = 15 m * 12 m = 180 m²
Lateral Faces:
Face 1: Area = (1/2) * base length * slant height = (1/2) * 15 m * 10 m = 75 m²
Face 2: Area = (1/2) * base length * slant height = (1/2) * 12 m * 10 m = 60 m²
Face 3: Area = (1/2) * base length * slant height = (1/2) * 15 m * 10 m = 75 m²
Face 4: Area = (1/2) * base length * slant height = (1/2) * 12 m * 10 m = 60 m²
Summing up the areas of all faces: Base Area + Lateral Faces Area = 180 m² + 75 m² + 60 m² + 75 m² + 60 m² = 450 m²
Therefore, the surface area of the rectangular pyramid is 450 m².
Rounded to the nearest hundredth, the surface area is 450.00 m².
The correct answer is 450.00 m².