Question

The cost of fencing a circular field at rs 11.50 per metre is rs 2350. The field is to be ploughed at the rate of RS 6.50 per m2. Find the cost of ploughing the field

Answer 1

ANSWER:-

Given:

The cost of fencing a circular field at Rs.11.50 per m is Rs.2350.

The field is to be ploughed at the rate of Rs.6.50 per m².

To find:

The cost of ploughing the field.

Solution:

Length of circular field;

$= > \frac{total \: cost}{rate} \\ \\ = > \frac{2350 \times 100}{11.50 \times 100} \\ \\ = > \frac{235000}{1150} \\ \\ = > 204.34m$

Let r be the radius of the field, then circumference= 204.34m

=) 2πr= 204.34

$= > 2 \times \frac{22}{7} \times r = 204.34 \\ \\ = > \frac{44}{7} \times r = 204.34 \\ \\ = > r = \frac{204.34 \times 7}{44} \\ \\ = > r = \frac{1430.38}{44} \\ \\ = > r = 32.5m$

Now,

Area of circular field= πr².

$= > (\frac{22}{7} \times 32.5 \times 32.5) {m}^{2} \\ \\ = > (3.14 \times 32.5 \times 32.5) {m}^{2} \\ \\ = > 3316.62 {m}^{2}$

So,

The cost of ploughing the field;

=) Rs.(3316.62 × 6.50)

=) Rs. 21558.03

Hence,

The cost of ploughing the field is Rs.21558.03.

Hope it helps ☺️