5. Rewriting Equations and Formulas
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The circumference of a circle is calculated using the formula C=2Ï€ r, where r is the radius.
Use the formula found in Part A.
The cross section of this column is a circle. What do you need to calculate the area of a circle?
r=C/2Ï€
1.1 feet, 1.3 feet, and 1.4 feet
See solution.
The circumference of a circle is calculated using the following formula, where r is the radius.
.LHS /2Ï€.=.RHS /2Ï€.
Simplify quotient
Rearrange equation
We found that the formula for the radius given the circumference is r= C2Ï€.
To calculate the radius of a column given its circumference, we need to substitute this circumference value for C into the formula found in Part A.
r=C/2Ï€
C= 7
Use a calculator
Round to 1 decimal place(s)
The radius of the given column is approximately 1.1 feet. We can summarize all the other findings in a table.
| C | C/2Ï€ | r |
|---|---|---|
| 7 | 7/2Ï€ | 1.1 |
| 8 | 8/2Ï€ | 1.3 |
| 9 | 9/2Ï€ | 1.4 |
We know that a cross section of a column is a circle. We are asked to explain how we can find the area of a circle when we know its circumference. First, recall the formula for the area of a circle.