carl has a box with a length width and height of 12 inches. she needs a box that is 4 inches longer, not as high, yet still has exactly the same width and volume.
what are the new dimensions?
which box requires more material to construct?
PLEASE HELP ME!! :(
Here is a start. Find volume, then new height.
12^3 = Volume = 12 * (12+4) * h
Original box = 12^2 * 5 = material.
New box = 12(12+4) + 2(12h) + 2(12+4)h = material
a volume is 864 what is the length width and height if length and width are the same and height is half of width and length
To find the new dimensions, we can start by determining the volume of the original box.
The volume of a box is calculated by multiplying its length, width, and height. In this case, the original box has a length, width, and height of 12 inches. So, the volume of the original box is:
Volume = Length * Width * Height = 12 * 12 * 12 = 1,728 cubic inches
Now, we need to find a box that is 4 inches longer but not as high while maintaining the same width and volume.
Let's assume the new length of the box is x inches. The new height can be represented as (12 - h), where h is the amount by which the original height is reduced.
So, the new volume can be calculated using the equations:
NewVolume = NewLength * Width * NewHeight
= x * 12 * (12 - h)
Since the new volume must be the same as the original volume, we can equate the two:
NewVolume = OriginalVolume
x * 12 * (12 - h) = 1,728
Now, we have an equation with two variables (x and h). We need another equation to solve for both variables.
We know that the new length is 4 inches longer than the original length:
x = 12 + 4
x = 16
Now, we can substitute this value of x into the equation:
16 * 12 * (12 - h) = 1,728
Simplifying the equation:
12 * (12 - h) = 108
Dividing both sides of the equation by 12:
12 - h = 9
Solving for h:
h = 12 - 9
h = 3
Therefore, the new dimensions are:
Length: 16 inches
Width: 12 inches (same as the original)
Height: 3 inches
To determine which box requires more material to construct, we can calculate the surface area of each box.
The surface area of the original box is given by:
Surface Area = 2*(Length*Width + Length*Height + Width*Height)
= 2*(12*12 + 12*12 + 12*12)
= 2*(144 + 144 + 144)
= 2*(432)
= 864 square inches
Similarly, the surface area of the new box is given by:
Surface Area = 2*(NewLength*Width + NewLength*NewHeight + Width*NewHeight)
= 2*(16*12 + 16*3 + 12*3)
= 2*(192 + 48 + 36)
= 2*(276)
= 552 square inches
Therefore, the original box requires more material to construct as it has a greater surface area (864 square inches compared to 552 square inches).