A rectangular park is $ 100 \mathrm{~m} $ by $ 50 \mathrm{~m} $. It is surrounded by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre (Use $ \pi=3.14) $.

Given: 

A rectangular park is \( 100 \mathrm{~m} \) by \( 50 \mathrm{~m} \). It is surrounded by semi-circular flower beds all round.

To do: 

We have to find the cost of levelling the semi-circular flower beds.

Solution:

Length of the rectangular park $l = 100\ m$

Breadth of the rectangular park $b= 50\ m$
Radius of each semicircular bed along the length side $r_1 =\frac{100}{2}=50\ m$

Radius of each semicircular bed along the breadth side $r_2 =\frac{50}{2}=25\ m$

Therefore,

Area of two semi-circles on length side $=2 \times \frac{1}{2} \pi \mathrm{r_1}^{2}$

$=3.14 \times(50)^{2} \mathrm{~m}^{2}$

$=3.14 \times 2500 \mathrm{~m}^{2}$

$=7850 \mathrm{~m}^{2}$

Area of two semi-circles on breadth side $=2 \times \frac{1}{2} \pi {r_2}^{2}$

$=3.14(25)^{2} \mathrm{~m}^{2}$

$=3.14 \times 625 \mathrm{~m}^{2}$

$=1962.5 \mathrm{~m}^{2}$

Total area of the beds $=7850+1962.5 \mathrm{~m}^{2}$

$=9812.5 \mathrm{~m}^{2}$

Rate of levelling the beds $=60$ paise per $\mathrm{m}^{2}$
Total cost of levelling the beds $=Rs.\ 9812.5 \times \frac{60}{100}$

$=Rs.\ 5887.50$

The cost of levelling the semi-circular flower beds is Rs. 5887.50.

Tutorialspoint

e

Updated on: 10-Oct-2022

49 Views

Kickstart Your Career

Get certified by completing the course

Get Started