A cardboard sheet is of rectanguler shape with dimensions 48m x 36m. From each of its corners,a square is cut off so as to make an open box. if the side of the square of the square is 8m, find the volume and lateral surface area of the box.
can you say homework dump?
I knew you could.
Still, here's a freebie. Show some effort on the rest, ok?
v = (48-16)(36-16)(8) = 5120 m^3
a = (48-16)(36-16) + 2((48-16)(8) + (36-16)(8)) = 1472 m^2
To find the volume and lateral surface area of the box, we need to consider the changes made to the cardboard sheet.
Step 1: Determine the dimensions of the box.
Since squares are cut from each corner, the length and width of the cardboard sheet will decrease by twice the side length of the square. Therefore, the length of the box will be 48m - 2(8m) = 48m - 16m = 32m, and the width will be 36m - 2(8m) = 36m - 16m = 20m.
Step 2: Calculate the volume of the box.
The volume of a box is given by the formula: Volume = length x width x height.
In this case, the height of the box is equal to the side of the square that was cut off, which is 8m.
Therefore, the volume of the box is: Volume = 32m x 20m x 8m = 5120 cubic meters.
Step 3: Calculate the lateral surface area of the box.
The lateral surface area of a box is the sum of the areas of its four sides.
The two longer sides have dimensions 32m x 8m, and the two shorter sides have dimensions 20m x 8m.
Therefore, the lateral surface area of the box is: Lateral Surface Area = 2(32m x 8m) + 2(20m x 8m) = 512 square meters.
So, the volume of the box is 5120 cubic meters and the lateral surface area is 512 square meters.