Solve the formula [tex]$C=\pi d$[/tex] for [tex]$d$[/tex].
A. [tex]$d=\frac{C}{\pi}$[/tex]
B. [tex]$d=C-\pi$[/tex]
C. [tex]$d=\frac{\pi}{C}$[/tex]
D. [tex]$d=\pi C$[/tex]
Answer (1)
Divide both sides of the equation by π to isolate d .
The result is d = π C .
Compare the result with the given options.
The correct answer is d = π C .
Explanation
Understanding the Formula We are given the formula C = π d , where C represents the circumference of a circle, d represents the diameter, and π is a constant approximately equal to 3.14159. Our goal is to isolate d on one side of the equation to solve for it in terms of C and π .
Isolating d To solve for d , we need to undo the multiplication by π . We can do this by dividing both sides of the equation by π :
π C = π π d π C = d So, we have d = π C .
Matching the Solution Now, we compare our result with the given options: A. d = π C B. d = C − π C. d = C π D. d = π C Our solution d = π C matches option A.
Examples
In real life, if you know the circumference of a circular object, like a pizza, you can find its diameter using this formula. For example, if a pizza has a circumference of 30 inches, its diameter would be approximately π 30 ≈ 9.55 inches. This is useful in various applications, from cooking to engineering, where knowing the diameter from the circumference is necessary.
