Question

The cost of fencing a circular plot at the rate of Rs.15 per m is ` 3300. What will be the cost of flooring the plot at the rate of Rs.100 per sq m ?

• A. Rs.385000
• B. Rs.220000
• C. Rs.350000
• D. Cannot be determined

Answer 1

The Correct Option is A

The problem involves calculating the total cost of flooring a circular plot given the cost and length of the fencing. Let's break down the steps to find the correct answer:

1. Determine the circumference of the plot: The cost of fencing the plot is Rs. 3300 at a rate of Rs. 15 per meter. The formula for the fencing cost is:

Cost of fencing = Circumference × Rate

Therefore, the circumference (\(C\)) can be calculated as follows:

\(C = \frac{\text{Cost of Fencing}}{\text{Rate per meter}}\)

\(C = \frac{3300}{15} = 220 \text{ m}\)

2. Find the radius of the plot using the circumference: The formula that relates circumference and radius (\(r\)) of a circle is:

\(C = 2\pi r\)

By substituting the known circumference:

\(220 = 2 \times \pi \times r\)

\(r = \frac{220}{2\pi}\)

\(r = \frac{110}{\pi}\) meters

3. Calculate the area of the plot: The formula for the area (\(A\)) of a circle is:

\(A = \pi r^2\)

Substituting the radius we found:

\(A = \pi \left(\frac{110}{\pi}\right)^2\)

\(A = \frac{110^2}{\pi} \times \pi\)

\(A = 110^2\)

\(A = 12100 \text{ sq m}\)

4. Calculate the cost of flooring: The cost of flooring is at the rate of Rs. 100 per square meter:

Cost of flooring = Area × Rate per sq m

\(Cost = 12100 \times 100\)

\(Cost = Rs.1210000\)

Hence, the cost of flooring the plot at the assumed area (decreased from the issue in initial options) is not matching Rs. 385000, indicating initial understanding or option error.

The cost expected with correct determination: Rs. 1210000