A rectangular solid with the dimension 1m x 1m x 3m is divided into three equal cubes. How much is the surface area of this solid increased?
you have added 2 sides at each juncture, or an additional area of 2*1+ 2*1 or 4m^2
So what does that mean? Sorry I don't understand. How do I find the percentage of increase?
percentage increase= 4m^2 over old surface area. Figure that out. add the total area for all six sides, and add. Draw a picture.
I am soooo confused!!
To find the surface area increase, we will need to calculate the surface area of the solid before and after it is divided into three equal cubes.
The initial surface area of the solid can be found by calculating the area of each face and summing them up. Since the solid is a rectangular prism with dimensions 1m x 1m x 3m, it has six faces, each with an area of (length x width).
Area of each face = 1m x 1m = 1 square meter
Total initial surface area = 6 faces x 1 square meter each = 6 square meters
When the solid is divided into three equal cubes, the three cubes will have dimensions of 1m x 1m x 1m each. To find the surface area of each cube, we calculate the area of each face and sum them up. Since each cube has six faces, the total surface area of the three cubes would be 6 times the surface area of one cube.
Surface area of each cube = 6 faces x (1m x 1m) = 6 square meters
Surface area of the three cubes = 3 cubes x 6 square meters each = 18 square meters
To find the increase in surface area, we subtract the initial surface area from the surface area of the three cubes.
Surface area increase = Surface area of the three cubes - Total initial surface area
Surface area increase = 18 square meters - 6 square meters
Surface area increase = 12 square meters
Therefore, the surface area of the rectangular solid increases by 12 square meters when it is divided into three equal cubes.