the largest doll is 7 inches tall. each of the other dolls is 1 inch shorter than the next larger doll. make a table that compares the surface areas and the volumes of the seven dolls.
To compare the surface areas and volumes of the seven dolls, we need to calculate them based on the given information that the largest doll is 7 inches tall and each of the other dolls is 1 inch shorter than the next larger doll. We'll create a table to organize the data.
First, let's define Doll 1 as the largest doll with a height of 7 inches. We'll use this as a base for calculating the surface areas and volumes of the other dolls.
Now, let's calculate the dimensions, surface areas, and volumes for each doll:
Doll | Height (inches) | Surface Area (inches^2) | Volume (inches^3)
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Doll 1 | 7 |
Doll 2 | |
Doll 3 | |
Doll 4 | |
Doll 5 | |
Doll 6 | |
Doll 7 | |
To calculate the height of each doll, we know that each doll is 1 inch shorter than the next larger doll. Therefore, the height of Doll 2 would be 7 - 1 = 6 inches. Similarly, the height of Doll 3 would be 6 - 1 = 5 inches, and so on.
Next, we'll calculate the surface area and volume of each doll based on their dimensions.
The surface area of a cylinder (which the dolls resemble) can be calculated using the formula:
Surface Area = 2πrh + 2πr^2, where r is the radius of the base and h is the height.
The volume of a cylinder can be calculated using the formula:
Volume = πr^2h.
Using these formulas and the dimensions we've calculated, we can now complete the table as follows:
Doll | Height (inches) | Surface Area (inches^2) | Volume (inches^3)
------------------------------------------------------------------------
Doll 1 | 7 | |
Doll 2 | 6 | |
Doll 3 | 5 | |
Doll 4 | | |
Doll 5 | | |
Doll 6 | | |
Doll 7 | | |
To calculate the surface area and volume of each doll, we need to know the radius of the base for each doll. However, the radius is not given in the problem statement. If the radius is not provided or if there is a specific relation between the dimensions of the dolls, we won't be able to calculate the exact surface area or volume.
I apologize for any confusion caused, but without more information, it is not possible to complete the table accurately. If you have any additional information or specific requirements, please provide them so that I can assist you further.
SA is proportional to the square of the height
V is proportional to the cube of the height