If the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2 , what is the height of this prism?(1 point)
A rectangular prism has a volume of 27 in.3 . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1 point)
To determine if the refrigerator will fit in the space, we need to calculate the volume of the refrigerator using the given dimensions:
Volume of the refrigerator = 76 cm * 76 cm * 170 cm = 976,160 cm^3
Since the volume of the refrigerator is 976,160 cm^3, which is greater than the available space of 975,000 cm^3, the refrigerator is too big for the space.
The correct response is:
No, it is 6,920 cm^3 too big for the space.
Apologies for the miscalculation earlier. Let's recalculate the volume for the refrigerator using the dimensions provided:
Volume of the refrigerator = 76 cm * 76 cm * 170 cm = 981,920 cm^3
Given that the space available has a volume of 975,000 cm^3, the refrigerator will not fit in the space as it is larger than the available space.
The correct response is:
No, it is 6,920 cm^3 too big for the space.
What is the volume of the rectangular pyramid?
An illustration shows a rectangular pyramid with length of 7.5 miles, a width of 7 miles, and a perpendicular height of 5 miles. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.
The volume of a rectangular pyramid is given by the formula:
V = (1/3) * base area * height
Given the dimensions of the rectangular pyramid as:
Length = 7.5 miles
Width = 7 miles
Perpendicular height = 5 miles
The base area of the rectangular pyramid is:
Base Area = Length * Width = 7.5 miles * 7 miles = 52.5 square miles
Now, substitute these values into the formula for the volume of a pyramid:
V = (1/3) * 52.5 * 5
V = (1/3) * 262.5
V = 87.5 cubic miles
The volume of the rectangular pyramid is 87.5 cubic miles.
Question
A slice of cheese is cut from a wheel of parmesan, and the wedge approximates the shape of a rectangular pyramid. Its base is 4 cm wide and 9 cm long. The wedge is 21 cm tall. What is the volume of the piece of cheese?(1 point)
To find the volume of the wedge-shaped slice of cheese, we can use the formula for the volume of a rectangular pyramid:
V = (1/3) * base area * height
Given:
Base width (w) = 4 cm
Base length (l) = 9 cm
Height (h) = 21 cm
First, calculate the base area:
Base Area = l * w
Base Area = 9 cm * 4 cm
Base Area = 36 square cm
Now, plug the base area and height into the volume formula:
V = (1/3) * 36 * 21
V = (1/3) * 756
V = 252 cubic cm
Therefore, the volume of the wedge-shaped slice of cheese is 252 cubic cm.
For a rectangular prism, the volume is given by the formula:
V_prism = l * w * h, where l, w, and h are the length, width, and height of the prism respectively.
Given that the volume of the prism is 27 in^3, we have V_prism = 27 in^3.
Now, it's mentioned that a rectangular pyramid with the same base and height as the prism is being considered. The volume of a rectangular pyramid is given by the formula:
V_pyramid = (1/3) * base area * h, where h is the height of the pyramid, and the base area is the same as the base of the prism, which is l * w.
Since the base and height of the pyramid are congruent to the prism, the base area of the pyramid is the same as the base area of the prism, which is l * w.
Substituting V_prism = 27 in^3 and base area = l * w into the formula for the pyramid, we get:
V_pyramid = (1/3) * V_prism
V_pyramid = (1/3) * 27
V_pyramid = 9 in^3
Therefore, the volume of the rectangular pyramid is 9 in^3.
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)
For a rectangular pyramid, the volume is given by the formula:
V_pyramid = (1/3) * base area * h, where h is the height of the pyramid, and the base area is the product of the base dimensions (length and width).
Given that the volume of the pyramid is 480 in^3, we have V_pyramid = 480 in^3.
Since the base and height of the rectangular prism are congruent to the pyramid, the base area of the prism is the same as the base area of the pyramid, which is the base area of the pyramid is b, then the base area of the prism is b as well.
Now, we know the volume of a rectangular prism is given by:
V_prism = base area * h
Substituting V_pyramid = 480 in^3 into the formula for the pyramid, we get:
480 = (1/3) * b * h
Since the base area and height of the pyramid are the same as that of the prism, the volume of the prism is:
V_prism = 3 * V_pyramid
V_prism = 3 * 480
V_prism = 1440 in^3
Therefore, the volume of the rectangular prism is 1440 in^3.
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?
An illustration shows a triangle with its base as 20 feet and its perpendicular height as 6 feet.
To find the volume of the pyramid given that both the prism and the pyramid have the same triangular base and height, we first calculate the base area of the triangle.
The base of the triangle is given as 20 feet, and the perpendicular height (corresponding to the height of the prism and pyramid) is given as 6 feet. The formula for the area of a triangle is:
Area = (1/2) * base * height
Substitute the values:
Base Area = (1/2) * 20 feet * 6 feet
Base Area = 60 square feet
Given that the volume of the prism is 600 ft^3 and the volume of a prism is calculated as:
V_prism = base area * height, where height is the height of the prism and pyramid.
We know that the volume of the prism is 600 ft^3, so let's substitute the known values:
600 = 60 * height
height = 10 feet
Now that we have the height of the pyramid, we can calculate the volume of the pyramid using the formula for the volume of a pyramid:
V_pyramid = (1/3) * base area * height
Substitute the values:
V_pyramid = (1/3) * 60 * 10
V_pyramid = 200 ft^3
Therefore, the volume of the pyramid is 200 ft^3.
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?
To find the volume of the composite figure formed by a rectangular prism with a cube placed on top, we first calculate the volume of each shape and then add them together.
1. Volume of the rectangular prism:
Given:
Length = 11 inches
Width = 3 inches (from the cube on top)
Height = 4 inches
The volume of the rectangular prism is calculated as:
Volume_prism = Length * Width * Height
Volume_prism = 11 in * 3 in * 4 in
Volume_prism = 132 cubic inches
2. Volume of the cube:
Since each side of the cube is 3 inches, the volume of the cube is given by:
Volume_cube = side^3 = 3^3 = 27 cubic inches
Now, to find the volume of the composite figure, we add the volumes of the rectangular prism and the cube:
Volume_composite = Volume_prism + Volume_cube
Volume_composite = 132 cubic inches + 27 cubic inches
Volume_composite = 159 cubic inches
Therefore, the volume of the composite figure formed by the rectangular prism with a cube placed on top is 159 cubic inches.
What is the volume of the composite figure?
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.
To find the volume of the composite figure formed by three rectangular prisms (two identical ones on the sides and one center prism), we need to calculate the volume of each prism and then add them together.
1. Volume of the two identical side prisms:
Given:
Length = 16 inches
Width = 7 inches
Height = 7 inches
The volume of each side prism is calculated as:
Volume_side_prism = Length * Width * Height
Volume_side_prism = 16 in * 7 in * 7 in
Volume_side_prism = 784 cubic inches
Since there are two identical side prisms, the total volume for both sides will be:
Total volume for side prisms = 2 * Volume_side_prism
Total volume for side prisms = 2 * 784 cubic inches
Total volume for side prisms = 1568 cubic inches
2. Volume of the center prism:
Given:
Length = 10 inches
Width = 8 inches
Height = 7 inches
The volume of the center prism is calculated as:
Volume_center_prism = Length * Width * Height
Volume_center_prism = 10 in * 8 in * 7 in
Volume_center_prism = 560 cubic inches
Now, to find the volume of the composite figure (inverted U-shaped structure), we add the volumes of the three prisms:
Total volume of the composite figure = Total volume for side prisms + Volume_center_prism
Total volume of the composite figure = 1568 cubic inches + 560 cubic inches
Total volume of the composite figure = 2128 cubic inches
Therefore, the volume of the composite figure formed by the three rectangular prisms is 2128 cubic inches.
Solve the problem. What is the volume of a rectangular pyramid with a base of 200 square meters and a height of 75 meters? Show your work.(2 points)
To find the volume of a rectangular pyramid, we can use the formula:
Volume of a rectangular pyramid = (1/3) * base area * height
Given:
Base area = 200 square meters
Height = 75 meters
Substitute these values into the formula:
Volume = (1/3) * 200 * 75
Volume = (1/3) * 15000
Volume = 5000 cubic meters
Therefore, the volume of the rectangular pyramid is 5000 cubic meters.
Can a refrigerator that is 21.5 cubic feet fit in a space that is 21 cubic feet? (1 point)
No, the refrigerator that is 21.5 cubic feet will not fit in a space that is 21 cubic feet. The refrigerator is larger than the available space, so it will not fit.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that the volume is 1.5 in^3 and the product of the length and width is 1.5 in^2, we have:
1.5 = lwh
And
l * w = 1.5
To find the height, we can rearrange the formula for volume to solve for height:
h = V / lw
Substitute the given values:
h = 1.5 / 1.5 = 1 in
Therefore, the height of the prism is 1 inch.
Lloyd bought a refrigerator that measures 76 cm×76 cm×170 cm to fit in a space with a volume of 975,000 cm3 . Will the refrigerator fit in the space? Explain.(1 point)
Responses
No, it is 6,920 cm3 too big for the space.
No, it is 6,920 cm cubed too big for the space.
Yes, it will fit. It will be a bit tight, but that won’t matter.
Yes, it will fit. It will be a bit tight, but that won’t matter.
No, it is 6,920 cm3 too small for the space.
No, it is 6,920 cm cubed too small for the space.
Yes, it will fit since it is smaller than the space.