To find the volume of the shape made by stacking four identical rectangular prisms, we first need to determine the dimensions of each prism.
Since all three rectangular prisms have an area of 648 square inches, let's assume the dimensions of one prism are length (L), width (W), and height (H), where:
L x W = 648 (Equation 1)
W x H = 648 (Equation 2)
L x H = 648 (Equation 3)
To find the values of L, W, and H, we can solve this system of equations. Notice that all three equations are equal to each other (648).
From Equation 1:
L x W = 648
Let's assume L = 8, W = 81 (these are factors of 648). Therefore, the dimensions of the first rectangular prism are 8 x 81.
From Equation 2:
W x H = 648
Using W = 81, H = 8. Therefore, the dimensions of the second rectangular prism are 81 x 8.
From Equation 3:
L x H = 648
Using L = 8, H = 81. Therefore, the dimensions of the third rectangular prism are 8 x 81.
Now, the shape made by stacking four identical prisms will have a length of 8 inches (L), a width of 81 inches (W), and a height of 4 times the height of one prism - 4 x 81 inches (4H).
Therefore, the dimensions of the exhibit shape are:
Length = 8 inches
Width = 81 inches
Height = 324 inches (4 x 81 inches)
To find the volume of this shape, we multiply the length, width, and height:
Volume = 8 inches x 81 inches x 324 inches
Volume = 209,088 cubic inches
Hence, the exhibit shape has a volume of 209,088 cubic inches.
There is 3 rectangular prisms and they all are 648 inch 2 now an art exhibit is made by stacking four identical prisms on top of eachother end to end so thier smallest faces overlap now find the exhibit of this shape
7 answers
Do he same thing exept stack 4 cubes so it's 4 cubes together see how this goes
If we stack four identical cubes together, we need to determine the volume of the resulting shape.
Let's assume the side length of one cube is "s". Therefore, the volume of one cube is s^3.
To find the total volume when four cubes are stacked, we need to consider the dimensions of the resulting shape.
When stacking four cubes on top of each other, the resulting height will be the sum of the heights of the four cubes. So, the height of the shape will be 4s.
The length and width of the shape will be the same as one cube, which is s.
Therefore, the dimensions of the shape are:
Length = s
Width = s
Height = 4s
To find the volume of this shape, we multiply the length, width, and height:
Volume = s x s x (4s)
Volume = 4s^3
So, the volume of the shape made by stacking four cubes together is 4s^3.
It's important to note that you would need to know the measurement of the side length, "s," in order to calculate the volume of the shape. Without that specific information, we cannot provide a numerical value for the volume.
Let's assume the side length of one cube is "s". Therefore, the volume of one cube is s^3.
To find the total volume when four cubes are stacked, we need to consider the dimensions of the resulting shape.
When stacking four cubes on top of each other, the resulting height will be the sum of the heights of the four cubes. So, the height of the shape will be 4s.
The length and width of the shape will be the same as one cube, which is s.
Therefore, the dimensions of the shape are:
Length = s
Width = s
Height = 4s
To find the volume of this shape, we multiply the length, width, and height:
Volume = s x s x (4s)
Volume = 4s^3
So, the volume of the shape made by stacking four cubes together is 4s^3.
It's important to note that you would need to know the measurement of the side length, "s," in order to calculate the volume of the shape. Without that specific information, we cannot provide a numerical value for the volume.
The in for width is 9 the length is 6 and the depth is 18 solve the surface area of t be rectangular prism
The formula to calculate the surface area of a rectangular prism is given by:
Surface Area = 2lw + 2lh + 2wh
Given that the width (w) is 9 inches, the length (l) is 6 inches, and the depth (h) is 18 inches, we can substitute these values into the formula to find the surface area.
Surface Area = 2(6)(9) + 2(6)(18) + 2(9)(18)
Surface Area = 108 + 216 + 324
Surface Area = 648 square inches
Therefore, the surface area of the rectangular prism is 648 square inches.
Surface Area = 2lw + 2lh + 2wh
Given that the width (w) is 9 inches, the length (l) is 6 inches, and the depth (h) is 18 inches, we can substitute these values into the formula to find the surface area.
Surface Area = 2(6)(9) + 2(6)(18) + 2(9)(18)
Surface Area = 108 + 216 + 324
Surface Area = 648 square inches
Therefore, the surface area of the rectangular prism is 648 square inches.
Now stack them end to end so thier smallest faces overlap sooo add 3 more of those ob top
If you stack four identical rectangular prisms on top of each other, end to end, with their smallest faces overlapping, the resulting shape will have a new height.
Given that the original rectangular prism has a width of 9 inches, length of 6 inches, and depth of 18 inches, let's calculate the dimensions of the stacked shape:
Original Shape Dimensions:
Length = 6 inches
Width = 9 inches
Height = 18 inches
When stacking four identical prisms, the new height of the shape will be the sum of the heights of each individual prism, which is 18 inches.
Therefore, the dimensions of the stacked shape are:
Length = 6 inches
Width = 9 inches
Height = 4 x 18 inches = 72 inches
To find the volume of this stacked shape, we multiply the length, width, and height:
Volume = 6 inches x 9 inches x 72 inches
Volume = 3888 cubic inches
Hence, the stacked shape formed by putting four identical rectangular prisms on top of each other will have a volume of 3888 cubic inches.
Given that the original rectangular prism has a width of 9 inches, length of 6 inches, and depth of 18 inches, let's calculate the dimensions of the stacked shape:
Original Shape Dimensions:
Length = 6 inches
Width = 9 inches
Height = 18 inches
When stacking four identical prisms, the new height of the shape will be the sum of the heights of each individual prism, which is 18 inches.
Therefore, the dimensions of the stacked shape are:
Length = 6 inches
Width = 9 inches
Height = 4 x 18 inches = 72 inches
To find the volume of this stacked shape, we multiply the length, width, and height:
Volume = 6 inches x 9 inches x 72 inches
Volume = 3888 cubic inches
Hence, the stacked shape formed by putting four identical rectangular prisms on top of each other will have a volume of 3888 cubic inches.