Question

A circular ground of diameter 63m. is to be trilpe fenced. If the rate of wire is Rs. 25 per meter, what will be the cost of fencing the fround?​

Answer 1

Solution!!

The diameter of the circular ground is given in the question. The ground has to be fenced thrice. The cost of fencing the ground is given in the question. We have to find the total cost of fencing the ground thrice.

Diameter = 63 m

Radius = Diameter ÷ 2

Radius = 63 ÷ 2

Radius = 31.5 m

As we all know that fencing is done on the boundaries of the ground, so we will find the circumference of the circular ground.

Circumference = 2πr

Circumference = 2 × (22/7) × 31.5 m

Circumference = (1386/7) m

Circumference = 198 m

Now, the 198 m is the distance that has to be fenced. We have to fence thrice so we will multiply the circumference by 3. Hence, we will know the total length of fencing which needs to be done.

Total length of fencing = 198 m × 3 = 594 m

Now, we know that,

Cost of fencing 1 metre = Rs 25

Cost of fencing 594 metre = Rs 25 × 594

Total cost of fencing = Rs 14850

Answer 2

Tip

To solve these type of questions, circumference of circle formula and finding the cost by unitary method is used. In a circle with diameter $d$, the circumference of circle is given by:

$= \: \pi d$

We know that $\pi$ has two values: $\dfrac{22}{7} \: (or) \: 3.14$. Let us take $\pi$ as $\dfrac{22}{7}$.

Solution

We are given that, the circular ground of diameter 63 m is to be triple fenced. From this, we can observe that, fencing the ground involves the whole inside part of circular ground, which is nothing but circumference of the circular ground.

Finding Circumference:

$= \: \pi d$

$= \: \dfrac{22}{7} \times 63$

$= \: 22 \times 9$

$= \: 198\:m$

Since the ground is triple fenced, we need to multiply the circumference with 3.

$= \: 198 \times 3$

$= \: 594\:m$

According to the question, we need to find cost of fencing the circular ground if rate of wire is Rs.25 per meter.

>> Cost of fencing 1 m = Rs.25

>> Cost of fencing 594 m = 594 × 25

>> Cost of fencing 594 m = Rs. 14,850

Final Answer

Hence, the cost of fencing the ground is Rs. 14,850.