Question

4. A school ground is in the shape of a circle with
radius 103 m. Four tracks each of 3 m wide has to be
constructed inside the ground for the purpose of
track events. Find the cost of constructing the track
at the rate of 50 per sq.m.
​

Answer 1

Step-by-step explanation:

Area of whole ground =πr²=22/7*103*103=10609πm²

radius R=103 width each of 4 tracks is 3m=4*3=12 is total.

area of inner circle=π(R-total width )²

22/7*(103-12)²=π(91)²=8281πm²

area of the 4tracks =10609π-8281π

=2322π= 7297.7m².

cost of constructing at the rate of 50/m²=50*7297.7=364,885 Rs.

Answer 2

Answer:

The cost of constructing the track  at the rate of 50 per sq.m. is Rs.365681.  

Step-by-step explanation:                  

Given : A school ground is in the shape of a circle with  radius 103 m. Four tracks each of 3 m wide has to be  constructed inside the ground for the purpose of  track events.

To find : The cost of constructing the track  at the rate of 50 per sq.m. ?

Solution :

A school ground is in the shape of a circle with  radius 103 m.

The area of the ground is $A=\pi r^2$

$A_G=\pi\times 103\times 103$

$A_G=10609\pi\ m^2$

Four tracks each of 3 m wide has to be  constructed inside the ground for the purpose of  track events.

Width of 4 tracks is $W=4\times 3=12$

Area of inner circle is $A_I=\pi(R-W)^2$

$A_I=\pi(103-12)^2$

$A_I=(91)^2\pi$

$A_I=8281\pi\ m^2\pi$

The area of four tracks is $A=10609\pi-8281\pi$

$A=2328\pi$

$A=7313.62\ m^2$

Cost of constructing at the rate of 50/m² is

$C=7313.62\times 50$

$C=Rs.365681$

Therefore, the cost of constructing the track  at the rate of 50 per sq.m. is Rs.365681.