A rectangular prism has a volume of 162 cubic centimeters. If the length, width, and height are reduced to 1/3 of their original size what will the new volume be?
ur mom
the volume will be reduced by a factor of (1/3)(1/3)(1/3) = 1/27
1/27
To find the new volume of the rectangular prism after reducing the length, width, and height to 1/3 of their original size, we can use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
Let's denote the original dimensions of the rectangular prism as follows:
- Original length = L
- Original width = W
- Original height = H
We are given that the original volume (V_orig) of the rectangular prism is 162 cubic centimeters:
V_orig = L x W x H = 162 cubic centimeters
Now, if the dimensions are reduced to 1/3 of their original size, we can express the new dimensions as follows:
- New length = L/3
- New width = W/3
- New height = H/3
To find the new volume (V_new) after reducing the dimensions, we substitute the new dimensions into the formula for volume:
V_new = (L/3) * (W/3) * (H/3)
Simplifying this expression, we get:
V_new = (LWH) / (3 * 3 * 3) = V_orig / (3^3)
Substituting the value of V_orig as 162 cubic centimeters, we can calculate the new volume:
V_new = 162 / (3^3) = 162 / 27 = 6 cubic centimeters
Therefore, the new volume of the rectangular prism after reducing the dimensions to 1/3 of their original size is 6 cubic centimeters.