Mary current refrigerator has a volume of 20ft. The space she has for the refrigerator is 26ft. What sizes of refrigerators should she consider
Mary should consider refrigerators with a volume of 26ft or less.
cubic feet
length in feet, ft
area in square feet, ft^2
volume in cubic feet, ft^3
These are units of measurement commonly used for measuring objects and space:
- Cubic feet (ft^3) is a unit of measurement used for volume. It is the amount of space that can be filled by a cube that is 1 foot on each side.
Example: A refrigerator might have a volume of 20 ft^3.
- Feet (ft) is a unit of measurement used for length, distance, or height. It is one-third of a yard or 12 inches.
Example: Mary's available space for a refrigerator is 26 ft long.
- Square feet (ft^2) is a unit of measurement used for area. It is the amount of space that can be covered by a square that is 1 foot on each side.
Example: Mary's kitchen floor might be 100 ft^2.
- Volume in cubic feet (ft^3) is a unit of measurement used for measuring the amount of space an object takes up in three dimensions.
Example: A container might have a volume of 10 ft^3.
By the way where that refrigerator will fit depends on the specific height and width and depth compared to the space available. It might have a volume less than we calculated ( 26 ft^3 ) but be too wide to fit between the cabinet and the wall.
That's correct! It's important to not only consider the volume of the refrigerator, but also the height, width, and depth when choosing a refrigerator that will fit in a specific space. Mary should measure the available space carefully and then look for refrigerators that have dimensions that will fit within that space.
To determine the sizes of refrigerators Mary should consider, we need to find the maximum size that can fit within the available space.
Given:
Current refrigerator volume = 20ft^3
Available space = 26ft
To find the sizes of refrigerators, we'll use the refrigerator volume as the limiting factor.
Step 1: Calculate the maximum size based on the current refrigerator volume:
Let's assume the dimensions of the current refrigerator are A x B x C.
Volume = A x B x C = 20ft^3
Step 2: Determine the maximum size based on the available space:
Let's assume the dimensions of the new refrigerator are X x Y x Z.
Available space = X x Y x Z = 26ft
Step 3: Solve for the possible sizes:
We have two equations:
A x B x C = 20ft^3 (equation 1)
X x Y x Z = 26ft (equation 2)
We need to find positive integer values for X, Y, and Z that satisfy equation 2 while maintaining the same volume as the current refrigerator (equation 1).
Possible sizes depend on how you want to distribute the available space:
Case 1: All dimensions are equal:
If we assume X = Y = Z and solve equation 2, we get:
X x X x X = 26ft,
X^3 = 26ft,
X ≈ ∛26ft ≈ 3ft.
So, in this case, the possible size of the refrigerator should be approximately 3ft x 3ft x 3ft.
Case 2: Different dimensions:
If we assume different dimensions for X, Y, and Z, we can try different combinations that satisfy equation 2. For example:
X = 2ft, Y = 2ft, Z = 6.5ft
X = 2.5ft, Y = 2.5ft, Z = 4ft
X = 1ft, Y = 3ft, Z = 8.67ft
These are just a few examples, and there might be other combinations that can fit within the available space while having the same volume as the current refrigerator.
In summary, Mary should consider refrigerators with a maximum size of approximately 3ft x 3ft x 3ft or different combinations that satisfy equation 2 and have the same volume as the current refrigerator.
To determine the sizes of refrigerators Mary should consider, we need to calculate the maximum volume a refrigerator can have based on the space available.
Since the space Mary has for the refrigerator is 26ft, we need to find a refrigerator with a volume that equals or is less than this space.
Given that Mary's current refrigerator has a volume of 20ft, any new refrigerator she considers should have a volume equal to or less than 20ft.
Therefore, Mary should consider refrigerators with a volume of 20ft or less.