The volume of a rectangular prism is 960 cubic inches. If the dimensions of the base are
doubled and the height remains the same to create a new prism, what will be the volume of
the new rectangular prism in cubic inches?
To find the volume of the new rectangular prism, we need to understand the relationship between the dimensions and volume of a rectangular prism.
The volume of a rectangular prism is calculated by multiplying the length, width, and height. Let's call the original dimensions of the base of the prism as length (L), width (W), and height (H).
So, the volume formula is: Volume = Length × Width × Height
Given that the volume of the original rectangular prism is 960 cubic inches, we have:
960 = L × W × H ........(Equation 1)
Now, let's consider the new dimensions, where the length and width of the base are doubled while the height remains the same.
The new length would be 2L, and the new width would be 2W, but the height would remain as H.
So, the volume of the new rectangular prism can be calculated using the new dimensions:
New Volume = New Length × New Width × Height
= (2L) × (2W) × H
= 4(L × W × H)
Now, we have the value for the volume of the original rectangular prism (960 cubic inches) from Equation 1, we can substitute it into the new volume equation:
New Volume = 4 × 960
= 3840 cubic inches
Therefore, the volume of the new rectangular prism will be 3840 cubic inches.
To find the volume of the new rectangular prism, we need to know the dimensions of the original prism.
Let's assume the original prism has a length (L), width (W), and height (H).
We are given that the volume of the original prism is 960 cubic inches. So we have:
Volume = L * W * H = 960 cubic inches
Now, we are told that the dimensions of the base (length and width) are doubled in the new prism, while the height remains the same.
Let's calculate the new dimensions:
New length = 2L
New width = 2W
Height remains the same = H
Now, let's calculate the volume of the new prism:
New volume = (2L) * (2W) * H
= 4(L * W * H)
= 4 * Volume of the original prism
= 4 * 960 cubic inches
= 3840 cubic inches
Therefore, the volume of the new rectangular prism will be 3840 cubic inches.
the area of the base will be multiplied by 4, since it will be changed from LW to
(2L)(2W) = 4LW
So, apply that to finding the new volume.