A rectangular pyramid has a volume of 480 in.3 . If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?(1 point)ghj
The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height. Given that the volume of the pyramid is 480 in^3, we know that:
480 = (1/3) * base area * height
Since the base and height of the rectangular prism are congruent to the pyramid, the base area and height of the prism will be the same as the pyramid. Therefore, the volume of the rectangular prism will also be given by the formula V = (1/3) * base area * height.
Since the volume of the prism is equal to the volume of the pyramid, the volume of the prism will also be 480 in^3.
Therefore, the volume of the rectangular prism is 480 in^3.
Use the image to answer the question.
An illustration shows a triangular pyramid and a triangular prism. The edges that are not visible are marked as dashed lines. The triangular pyramid has the triangular face as its base. The sides of of the triangular base measure 3 inches and 5 inches. The perpendicular height of the pyramid is 8.41 inches. The triangular prism has its triangular face as the base. The sides of the triangular base measure 3 inches and 5 inches. The length of the side is 8.41 inches.
Which shape has the larger volume? How much larger is it?
(1 point)
Responses
The prism has a larger volume by 13 times.
The prism has a larger volume by Start Fraction 1 over 3 End Fraction times.
The prism has a larger volume by three times.
The prism has a larger volume by three times.
The volumes are the same.
The volumes are the same.
The pyramid has a larger volume by three times.
In this case, the volume of the pyramid and the prism can be found using the formula V = (1/3) * base area * height for the pyramid, and V = base area * height for the prism.
1. For the pyramid:
Base area = 0.5 * 3 * 5 = 7.5 in^2
Volume = (1/3) * 7.5 * 8.41 = 20.025 in^3
2. For the prism:
Base area = 0.5 * 3 * 5 = 7.5 in^2
Volume = 7.5 * 8.41 = 63.075 in^3
Therefore, the prism has a larger volume than the pyramid by a factor of 63.075 / 20.025 = 3 times.
Therefore, the correct response is:
The prism has a larger volume by three times.
Use the image to answer the question.
An illustration shows a triangle with its base as 20 feet and its perpendicular height as 6 feet.
A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 600 ft.3 , what is the volume of the pyramid?
(1 point)
Responses
200 ft.3
200 ft. cubed
400 ft.3
400 ft. cubed
600 ft.3
600 ft. cubed
1,800 ft.3
When a prism and a pyramid have the same base and height, the ratio of their volumes is given by 1:3. This means that the volume of the pyramid will be 1/3 of the volume of the prism.
Given that the volume of the prism is 600 ft^3, the volume of the pyramid will be:
Volume of the pyramid = (1/3) * 600 ft^3 = 200 ft^3
Therefore, the volume of the pyramid is 200 ft^3.
The correct response is:
200 ft.3
Use the image to answer the question.
An illustration shows a rectangular prism with a cube placed on top. The cube is 3 inches on all sides. The rectangular prism is 11 inches long and 4 inches high.
What is the volume of the composite figure?
(1 point)
To find the volume of the composite figure made up of the rectangular prism and the cube, we need to find the volumes of each shape separately and then add them together.
1. Volume of the rectangular prism:
Length = 11 inches
Width = 3 inches
Height = 4 inches
Volume = Length x Width x Height
Volume = 11 x 3 x 4 = 132 cubic inches
2. Volume of the cube:
Side length = 3 inches
Volume = Side length^3
Volume = 3^3 = 27 cubic inches
Now, add the volumes of the rectangular prism and the cube to get the total volume of the composite figure:
Total Volume = Volume of prism + Volume of cube
Total Volume = 132 + 27 = 159 cubic inches
Therefore, the volume of the composite figure is 159 cubic inches.
Use the image to answer the question.
An illustration shows an inverted U-shaped structure made up of three rectangular prisms. Two identical rectangular prisms are placed on either side of a center rectangular prism. The side prisms are 16 inches long, 7 inches wide, and 7 inches high. The prism placed in between the two rectangles is 8 inches wide and 10 inches long.
What is the volume of the composite figure?
(1 point)
To find the volume of the composite figure made up of the three rectangular prisms, we need to find the volumes of each prism separately and then add them together.
1. Volume of the side rectangular prisms:
Length = 16 inches
Width = 7 inches
Height = 7 inches
Volume = Length x Width x Height
Volume = 16 x 7 x 7 = 784 cubic inches for each side prism
2. Volume of the center rectangular prism:
Length = 10 inches
Width = 8 inches
Height = 7 inches
Volume = Length x Width x Height
Volume = 10 x 8 x 7 = 560 cubic inches for the center prism
Now, add the volumes of the side prisms and the center prism to get the total volume of the composite figure:
Total Volume = 2 * Volume of side prism + Volume of center prism
Total Volume = 2 * 784 + 560 = 2168 cubic inches
Therefore, the volume of the composite figure is 2168 cubic inches.
Volume Unit Test
13 of 1513 of 15 Items
Question
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An illustration shows a center-pedestal type table with the table top placed on vertical rectangular block that has a rectangular base. The table top length and width are 30 inches, with a depth of 2 inches. The height of the rectangular block pedestal is 25 inches, and the width and length are 8 inches each. The length and width of the rectangular base are 12 inches each, and the height is 4 inches. The table top has a checkerboard pattern.
What is the volume of the table?
(1 point)