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.