Question

A racing track has a horizontal part with semicircular ends. If the width of the track is 7 m and inner radius of semicircular part is 35 m and horizontal part is 14 m long find the cost of leveling the track at rs.12/m2 .

Answer 1

Answer:

Hence, cost of leveling the track is =₹ 22661.52

Step-by-step explanation:

The area of the track is calculated as:

( Area of rectangle ABCD+Area of 2 outer semicircles)-( Area of rectangle EFGH+Area of 2 inner semicircles)

We know that area of semicircle with radius 'r' is given as: $\dfrac{\pi r^2}{2}$

Area of 2 outer semicircle with radius 42 m is given by:

$2\times \dfrac{\pi\times 42\times 42}{2}\\\\=\pi\times 42\times 42\\\\=3.14\times 1764\\\\=5538.96m^2$

Area of 2 inner semicircles with radius 35 m is:

$2\times \dfrac{\pi\times 35\times35}{2}\\\\=\pi\times 35\times 35\\\\=3.14\times 1225\\\\=3846.5m^2$

Area of rectangle ABCD with dimensions 84 m×14 m is:

$=84\times 14\\\\=1176m^2$

Area of rectangle EFGH  with dimensions 70 m×14 m is:

$70\times 14\\\\=980m^2$

Hence, Area of track is:

$(1176+5538.96)-(980+3846.5)\\\\=1888.46m^2$

Now cost of leveling 1 m^2 of track=₹ 12

Hence, cost of leveling 1888.46 m^2=₹ (12×1888.46)

                                                            =₹ 22661.52