Question

The circumference of a circle varies directly with its radius. if the circumference of a circle with a radius of 1.5 inches is 9.42 in, what is the circumference of a circle with a radius of 9 in? use π = 3.14. round your answer to the nearest inch.

Answer 1

Answer: 57 in.

Step-by-step explanation:

When two quantities x and y are directly proportional , then the equation to show direct proportion is given  y :-

$\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}$      (1)

Given : The circumference of a circle varies directly with its radius.

Let c be the circumference of a circle with a radius of 9 in.

If the circumference of a circle with a radius of 1.5 inches is 9.42 in, then from (1) we have

$\dfrac{c}{9}=\dfrac{9.42}{1.5}\\\\\Rightarrow\ c=\dfrac{9.42}{1.5}\times9=56.52\approx57\ in.$

Hence, the circumference of a circle with a radius of 9 in is approximately 57 in.

Answer 2

 1) Circumference = 2πr 
C = 2 x π x 9 
C = 18π = 56.548... = 57 inches (to the nearest inch) 

2) 6h = $52.50 
1h = $52.50/6 = 8.75 
11h = 8.75 x 11 = $96.25 = $96 (to the nearest cent)