Question

The ratio of the area of a circle to the circumference of a​ circle, A/C, is 15/1 Find the circumference of the circle.

Answer 1

Answer:

The Circumference is 60π

Step-by-step explanation:

Solution :

Ratio of area of circle to circumference of circle = 15 : 1

Circumference of circle = 2πr

Area of circle = πr²

Here,

• r = radius
• π = pi

⇒ $\sf{\dfrac{A}{C} = \dfrac{{nr}^{2}}{(2\pi \: r)}}$

⇒ $\sf{\dfrac{15}{1} = \dfrac{{nr}^{2}}{(2\pi \: r)}}$

⇒ 15 = $\sf{\dfrac{r}{2}}$

⇒ 30 = r

Place in this value of r into the formula for circumference.

⇒ C = 2π(30)

⇒ C = 60π

Therefore, the Circumference is 60π

Answer 2

$\huge\sf{Answer:}$

☆ Given:

⇏ The ratio of the area of a circle to the circumference of a circle, $\sf \dfrac{A}{C}$ is $\sf \dfrac{15}{1}.$

☆ Find:

⇏ Find the circumference of the circle.

☆ According to the question:

⇏ The ratio of circle = 5:1 = [ $\sf \dfrac{5}{1}$ ].

☆ Using formula:

⇏ Circumference of circle = 2πr

⇏ Area of circle = πr²

☆ Calculations:

⇏ $\sf \dfrac{A}{C} = \dfrac{\pi r^2}{2 \: \pi r}$

⇏ $\sf \dfrac{15}{1} = \dfrac{\pi r^2}{2 \: \pi r}$

⇏ $\sf 15 = \dfrac{r}{2}$

⇏ $\sf r = 30$

☆ Finding the circumference using the above value:

⇏ $\sf Circumference = 2 \pi (r)$

⇏ $\sf Circumference = 2 \pi (30)$

⇏ $\sf Circumference = (2 \times 30)$

⇏ $\sf Circumference = 60 \pi$

Therefore, 60π is the circumference of the circle.