Hat sizes are determined by measuring the circumference of the head in either inches or centimeters?
use ratio and proportions to complete the following table
Hat size =7 Head circumference inches = 22 and Centimeters =56
and If hat size was 6 3/4 Head circumference in inches would = ? and in centimeters would = ?
Size 7 --> 22 in --> 56 cm
Size 1 --> 22/7 in (3.14 in) --> 56/7 cm (8 cm)
Thus:
Size 6 3/4 --> 3.14 * 6 3/4 in --> 8 * 6 3/4 cm
= about 21.2 in. --> 54 cm
To use ratios and proportions to complete the table, we need to establish a relationship between hat size and head circumference. Let's start by finding the ratio of head circumference to hat size for the given example.
In the first row, we have:
Hat size = 7
Head circumference (in inches) = 22
Head circumference (in centimeters) = 56
To find the ratio:
Ratio (in inches) = Head circumference (in inches) / Hat size
Ratio (in inches) = 22 / 7
Ratio (in centimeters) = Head circumference (in centimeters) / Hat size
Ratio (in centimeters) = 56 / 7
Let's calculate these ratios:
Ratio (in inches) = 3.14 (rounded to two decimal places)
Ratio (in centimeters) = 8 (rounded to the nearest whole number)
Now, we can use these ratios to complete the table for the given example:
| Hat size | Head circumference (in inches) | Head circumference (in centimeters) |
|----------|-------------------------------|------------------------------------|
| 7 | 22 | 56 |
| 6 3/4 | ? | ? |
To find the head circumference for hat size 6 3/4, we can use the ratios we calculated earlier.
Head circumference (in inches) = Hat size x Ratio (in inches)
Head circumference (in inches) = (6 + 3/4) x 3.14
Let's calculate it:
Head circumference (in inches) = 6.75 x 3.14 = 21.365 (rounded to two decimal places)
Head circumference (in centimeters) = Hat size x Ratio (in centimeters)
Head circumference (in centimeters) = (6 + 3/4) x 8
Let's calculate it:
Head circumference (in centimeters) = 6.75 x 8 = 54 (rounded to the nearest whole number)
Therefore, for hat size 6 3/4, the head circumference would be approximately 21.37 inches and 54 centimeters.