is it possible for two boxes to have the same volume, but different surface area's? give examples to prove your point.
please help, cannot think of anything. THANKS =]
Of course. Take a cube of 1 meter per edge, volume =1 cubic meter, Area=6m^2
Now take a box, bottom edges and top edges of 1/2 m, an height of 4 meters. Volume=1m^2, but Sarea=2*1/4 + 4*4*1/2=you do it. Notice the rectangular box has much more surface area for the same volume.
ohhhhh thanks bobpursley! you really made it more clearer then we tried to! :P
Yes, it is indeed possible for two boxes to have the same volume but different surface areas. The volume of a box is a measure of the amount of space inside the box, whereas the surface area is the measure of the total area covered by the box.
To prove this, let's consider two different shapes - a cube and a rectangular prism.
Example 1:
Cube A has sides of length 2 units. The volume of the cube can be calculated by V = s^3, where s is the length of a side. So, the volume of cube A is 2^3 = 8 cubic units. The surface area of a cube can be calculated by A = 6s^2, so the surface area of cube A is 6(2^2) = 24 square units.
Example 2:
Rectangular prism B also has a volume of 8 cubic units, but its dimensions are different. Let's say one dimension is 1 unit, another is 2 units, and the third dimension is 4 units. The volume of the rectangular prism is calculated by V = lwh, where l, w, and h are the length, width, and height, respectively. So, the volume of prism B is 1 x 2 x 4 = 8 cubic units. Now, the surface area of a rectangular prism can be calculated by A = 2lw + 2lh + 2wh. For prism B, the surface area would be 2(1x 2) + 2(1 x 4) + 2(2 x 4) = 2 + 8 + 16 = 26 square units.
In this example, both the cube and the rectangular prism have the same volume of 8 cubic units, but the cube has a surface area of 24 square units, while the rectangular prism has a surface area of 26 square units. Therefore, we've shown that it is possible for two boxes to have the same volume but different surface areas.