Question

a rectangular park is 70m by 56m it is surrounded by semi-circular flower beds all around. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre

Answer 1

Answer:

The cost of levelling the flower bed is Rs. 3581 . 46

Step-by-step explanation:

Given: A rectangular park is 70m by 56m it is surrounded by semi-circular flower beds

To find: The cost of levelling the flower bed

Solution

Length of the park = 70 m

Breadth of the park = 56 m T

he radius of the semi-circular flower beds = half of the corresponding side of the rectangular park

Radius of the bigger flower bed = 70/2 = 35 m

The radius of the smaller flower bed = 56/2 = 26 m

Total area of the flower bed = 2 [Area of bigger flower bed + Area of the

                                                            smaller flower bed

                                                =2 [ $\frac{1}{2} \pi r^{2} +\frac{1}{2} \pi r^{2}$]

We know that Area of the rectangle = $\frac{1}{2} \pi r^{2}$

Total area of the flower bed =   2 [ $\frac{1}{2} \pi r^{2} +\frac{1}{2} \pi r^{2}$]

                                              = 2 [$\frac{1}{2} \pi (35)^{2} +\frac{1}{2} \pi (26)^{2}$

                                             = 2 ×$\frac{1}{2}$ π[1225 +676}

                                               = π[1901]

                                                = 3.14  × 1901

                                                = Rs. 5969.14 $m^{2}$

Rate of levelling flower bed = 60 paise per $m^{2}$

The total cost of levelling = Rs. 5969.14 $m^{2}$ × 60

                                          = 358146 paise

The total cost of levelling = Rs . 3581 . 46

Final answer:

The total cost of levelling the flower bed is Rs. 3581 .46

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Answer 2

Answer:

Given: A rectangular park is 70m by 56m it is surrounded by semi-circular flower beds all around

To find: The cost of levelling the semi-circular flower beds at 60 paise per square meter

Step-by-step explanation:

The radius of the flower beds 1 and 2= 70/2

​=35m

⇒  Area of the flower beds given 1 and 2 =2×( $\frac{1}{2}$$\pi$$r^{2}$ )

⇒  Area of the flower beds given 1 and 2 =3.14×35×35=

=$3846.5m^{2}$

⇒  The radius of the flower beds 3 and 4 = 56/2

=28m

⇒  Area of the flower beds 3 and 4 = $2 *( \frac{1}{2}$$r^{2} )$

⇒  Area of the flower beds 3 and 4 =3.14×28×28= $2461.76m^{2}$

⇒  Area of the all four flower beds =3846.5$m^{2}$ +2461.76$m^{2}$

=6308.26$m^{2}$

⇒  Cost of levelling four flower beds =6308.26×0.60=Rs.5323.556$m^{2}$

∴The correct answer is Rs.5323.556$m^{2}$.

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