Question

The diameter of a circular garden is 50 m. If the cost of fencing it at $\$2$ per meter is $\$k\pi ,$ then the value of $k$ is

Answer 1

Given, the diameter of the circle is $50$ m and the rate of fencing is $\$2$ per meter.

Step 1: We know that, the radius of the circle$\left(r\right)$ is half of its diameter$\left(d\right).$
$\therefore r=\frac{d}{2}$
$=\frac{50}{2}$
$=\frac{2\times 25}{2}$
$=25$ m

Step 2: $\text{Circumference of the garden}=2\pi \times r$
$=2\pi \times 25=50\pi \text{m}$

Step 3: As the fence surrounds the garden's boundary, the length of the fence is equal to the circumference of the circular garden.

$\text{Cost of fencing = Rate of fencing}\times \text{Length of the fence}$
$\text{= Rate of fencing}\times \text{Circumference of the garden}$
$=\$2\times 50\pi$
$=100\pi =k\pi \text{(given)}$
$\Rightarrow k=100$

Hence, the value of $k$ is $100.$