Right Rectangular Prisms & Pyramids Unit Test
13 answers
I'm sorry, but as an AI language model, I am not able to administer or grade tests. I can, however, assist you with any concepts or questions you may have related to right rectangular prisms and pyramids.
Which of these everyday objects has the attributes of a right rectangular prism?
a book
a slice of cake
a house
shopping cart
a book
a slice of cake
a house
shopping cart
Among the given options, the everyday object that has the attributes of a right rectangular prism is a book. A book typically has a rectangular shape with six rectangular faces, making it a solid object with parallel and perpendicular sides. The other options, such as a slice of cake, a house, and a shopping cart, do not have the precise attributes of a right rectangular prism.
What is the surface area of a right rectangular prism where each edge length measures 15.10 cm?
900 cm^2
1,368.06 cm^2
8,208.36 cm^2
1,350 cm^2
900 cm^2
1,368.06 cm^2
8,208.36 cm^2
1,350 cm^2
To find the surface area of a right rectangular prism, you need to calculate the sum of the areas of all its faces.
In this case, all the edge lengths are 15.10 cm. Hence, the length, width, and height of the prism are all 15.10 cm.
The surface area can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the given values:
Surface Area = 2(15.10)(15.10) + 2(15.10)(15.10) + 2(15.10)(15.10)
Surface Area = 2(228.01) + 2(228.01) + 2(228.01)
Surface Area = 456.02 + 456.02 + 456.02
Surface Area = 1368.06 cm^2
Therefore, the correct answer is 1,368.06 cm^2.
In this case, all the edge lengths are 15.10 cm. Hence, the length, width, and height of the prism are all 15.10 cm.
The surface area can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the given values:
Surface Area = 2(15.10)(15.10) + 2(15.10)(15.10) + 2(15.10)(15.10)
Surface Area = 2(228.01) + 2(228.01) + 2(228.01)
Surface Area = 456.02 + 456.02 + 456.02
Surface Area = 1368.06 cm^2
Therefore, the correct answer is 1,368.06 cm^2.
Use the rubix cube image to solve the question.
Given that each square is 1 inch, find the surface area of this puzzle game.
Given that each square is 1 inch, find the surface area of this puzzle game.
I'm sorry, but as an AI language model, I don't have access to visual images or the ability to directly analyze or manipulate them. To determine the surface area of a Rubik's Cube, which consists of multiple squares, we need to know the number of squares on each face or the dimensions of the cube.
Without that information, it is not possible to calculate the surface area. However, a standard Rubik's Cube has six faces, each consisting of 9 squares (3x3). So, if each square is 1 inch, the surface area of a standard Rubik's Cube would be 6 x 9 = 54 square inches.
Without that information, it is not possible to calculate the surface area. However, a standard Rubik's Cube has six faces, each consisting of 9 squares (3x3). So, if each square is 1 inch, the surface area of a standard Rubik's Cube would be 6 x 9 = 54 square inches.
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?
3,420 in.^2
96 in.^2
725.75 in.^2
1,451.5 in^2
3,420 in.^2
96 in.^2
725.75 in.^2
1,451.5 in^2
To find the surface area of the carry-on suitcase, we need to calculate the sum of the areas of all its faces.
The given dimensions are length = 9.5 inches, width = 16 inches, and height = 22.5 inches.
The surface area can be calculated using the formula: Surface Area = 2lw + 2lh + 2wh.
Substituting the given values:
Surface Area = 2(9.5)(16) + 2(9.5)(22.5) + 2(16)(22.5)
Surface Area = 304 + 427.5 + 720
Surface Area = 1451.5 in^2
Therefore, the correct answer is 1,451.5 in^2.
The given dimensions are length = 9.5 inches, width = 16 inches, and height = 22.5 inches.
The surface area can be calculated using the formula: Surface Area = 2lw + 2lh + 2wh.
Substituting the given values:
Surface Area = 2(9.5)(16) + 2(9.5)(22.5) + 2(16)(22.5)
Surface Area = 304 + 427.5 + 720
Surface Area = 1451.5 in^2
Therefore, the correct answer is 1,451.5 in^2.
Lizzie and her wife need to paint the walls of their bedroom. The room is 12 feet by 14 feet, and it has a ceiling that is 10 feet high. What is the area that they need to paint?
To find the area that Lizzie and her wife need to paint, we need to calculate the total surface area of the walls.
The given dimensions are length = 12 feet, width = 14 feet, and height = 10 feet.
To calculate the area, we need to consider the walls without windows or doors. In this case, we need to find the area of the four walls.
The area of each wall can be calculated by multiplying the height by the width:
Wall 1: Height * Length = 10 feet * 12 feet = 120 square feet
Wall 2: Height * Length = 10 feet * 12 feet = 120 square feet
Wall 3: Height * Width = 10 feet * 14 feet = 140 square feet
Wall 4: Height * Width = 10 feet * 14 feet = 140 square feet
The total area that they need to paint is the sum of the areas of all four walls:
Total Area = Wall 1 + Wall 2 + Wall 3 + Wall 4
Total Area = 120 square feet + 120 square feet + 140 square feet + 140 square feet
Total Area = 520 square feet
Therefore, Lizzie and her wife need to paint an area of 520 square feet.
The given dimensions are length = 12 feet, width = 14 feet, and height = 10 feet.
To calculate the area, we need to consider the walls without windows or doors. In this case, we need to find the area of the four walls.
The area of each wall can be calculated by multiplying the height by the width:
Wall 1: Height * Length = 10 feet * 12 feet = 120 square feet
Wall 2: Height * Length = 10 feet * 12 feet = 120 square feet
Wall 3: Height * Width = 10 feet * 14 feet = 140 square feet
Wall 4: Height * Width = 10 feet * 14 feet = 140 square feet
The total area that they need to paint is the sum of the areas of all four walls:
Total Area = Wall 1 + Wall 2 + Wall 3 + Wall 4
Total Area = 120 square feet + 120 square feet + 140 square feet + 140 square feet
Total Area = 520 square feet
Therefore, Lizzie and her wife need to paint an area of 520 square feet.
A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work.
The formula for the volume of a rectangular pyramid is given by:
Volume = (1/3) * base area * height
We are given the length as 7 cm, width as 9 cm, and the volume as 231 cubic centimeters.
Let's denote the height of the pyramid as h.
Now, we need to calculate the base area of the pyramid. The base of a rectangular pyramid is a rectangle, and its area is given by multiplying the length and width:
Base Area = length * width
Base Area = 7 cm * 9 cm
Base Area = 63 square cm
Now we can set up the equation for the given volume and solve for the height:
231 cubic cm = (1/3) * 63 square cm * h
To solve for h, we can isolate it by multiplying both sides of the equation by 3 and then dividing by the base area:
231 cubic cm * 3 = 63 square cm * h
693 cubic cm = 63 square cm * h
693 cubic cm / 63 square cm = h
h = 11 cm
Therefore, the height of the rectangular pyramid is 11 cm.
Volume = (1/3) * base area * height
We are given the length as 7 cm, width as 9 cm, and the volume as 231 cubic centimeters.
Let's denote the height of the pyramid as h.
Now, we need to calculate the base area of the pyramid. The base of a rectangular pyramid is a rectangle, and its area is given by multiplying the length and width:
Base Area = length * width
Base Area = 7 cm * 9 cm
Base Area = 63 square cm
Now we can set up the equation for the given volume and solve for the height:
231 cubic cm = (1/3) * 63 square cm * h
To solve for h, we can isolate it by multiplying both sides of the equation by 3 and then dividing by the base area:
231 cubic cm * 3 = 63 square cm * h
693 cubic cm = 63 square cm * h
693 cubic cm / 63 square cm = h
h = 11 cm
Therefore, the height of the rectangular pyramid is 11 cm.
5 answers