a metallic sheet is of rectangular shape with dimensions 28m×36m from each of its corners a square is cut off so as to make an open box the volume of the box is Xm^3 , whenthe length of the square is 8m the value of X is?
width of base = 28-16 = 12 m
length of base = 36-16 = 20 m
height of box = 8 m
volume = 12(20)(8) = 1920 m^3
(why introduce variables when there is no need for them ?)
To find the volume of the box, we need to determine its dimensions.
Let's start by calculating the dimensions of the base of the box.
Since squares are cut off from each corner of the rectangular sheet, the length and width of the base will be reduced by twice the length of the square.
Given that the rectangular sheet has dimensions 28m × 36m, and the length of the square is 8m, we can calculate the dimensions of the base as follows:
Length of the base = Length of the rectangular sheet - 2 * Length of the square = 28m - 2 * 8m = 28m - 16m = 12m
Width of the base = Width of the rectangular sheet - 2 * Length of the square = 36m - 2 * 8m = 36m - 16m = 20m
Now we have the dimensions of the base: 12m × 20m.
Since the box is open, the height will be equal to the length of the square that was cut off, which is given as 8m.
Therefore, the dimensions of the box are 12m × 20m × 8m.
To calculate the volume, we multiply the three dimensions:
Volume = Length × Width × Height = 12m × 20m × 8m = 960 cubic meters.
Therefore, the value of X is 960 cubic meters.