Volume and surface area are often compared by manufacturers in order to
maximize how much of something can go inside of a package (volume) while
keeping how much material is required to create the package (surface area) low.
Pick a product that might be packaged in the shape of a rectangular prism. A
rectangular prism has three dimensions: length, width, and height. The surface
area of a rectangular prism can be found using the formula SA = 2lw + 2wh + 2lh.
The volume of a rectangular prism can be found using the formula V = lwh. Write
an expression for the ratio of surface area to volume for the figure.
Choose an appropriate length, width, and height for your package so that it can fit
the product you are shipping. Using these dimensions, what is the ratio of surface
area to volume?
no
To find the ratio of surface area to volume for a rectangular prism, we need to calculate both the surface area and the volume.
Let's assume the length (l) of the rectangular prism is 10 units, the width (w) is 5 units, and the height (h) is 3 units.
To calculate the surface area (SA) of the rectangular prism, we use the formula:
SA = 2lw + 2wh + 2lh
Substituting the given values:
SA = 2 * 10 * 5 + 2 * 5 * 3 + 2 * 10 * 3
SA = 100 + 30 + 60
SA = 190 square units
To calculate the volume (V) of the rectangular prism, we use the formula:
V = lwh
Substituting the given values:
V = 10 * 5 * 3
V = 150 cubic units
Now, let's find the ratio of the surface area to volume by dividing the surface area by the volume:
Ratio = SA / V
Ratio = 190 / 150
Ratio = 1.27
Therefore, the ratio of surface area to volume for the given dimensions is approximately 1.27.
To find the ratio of surface area to volume for a rectangular prism, we need to first express the surface area and volume formulas in terms of the dimensions.
Let's assume the length of the rectangular prism is 10 units, the width is 5 units, and the height is 3 units.
Surface area (SA) = 2lw + 2wh + 2lh
SA = 2(10)(5) + 2(5)(3) + 2(10)(3)
SA = 100 + 30 + 60
SA = 190 square units
Volume (V) = lwh
V = (10)(5)(3)
V = 150 cubic units
Now, we can find the ratio of surface area to volume by dividing the surface area by the volume:
Ratio = SA / V
Ratio = 190 / 150
Ratio ≈ 1.27
Therefore, the ratio of surface area to volume for this rectangular prism is approximately 1.27.
What did you choose?
How about a box of chocolate candy?