Question

A circular field, 28 m in diameter, has a path 1.75 m wide running round it on the outside.
Find the cost
of gravelling the path at 5 per square metre.​

Answer 1

Solution:

Given,

radius of circular field = 14m(OA)(r1)

Width of the path = 1.75m(AD)

REFER TO ATTACHMENT for diagram

So ,

radius OD = 14+1.75 =15.75 m(r2)

Remember,

area of circle = πr^2

Now, According to question

area of gravel path =

area of circle with radius OD -

area of circle with radius OA

=> π(r1)^2 - π( r2)^2

=>π{(r1)^2 - (r2)^2}

=>π{(15.75)^2 - (14)^2}

=>π(248.0625 - 196)

=>π(52.0625)

=>(22×52.0625)7 (since π =22/7)

=>163.625 m^2

hence area of the path is 163.625 m^2.

Now, cost of gravelling per square meter path = Rs 10

So, Cost of gravelling the163.625 m^2 path

= 163.625 × 10

=Rs1636.25

hence ,cost of gravelling the path is Rs1636.25.

Answer 2

Step-by-step explanation:

Area of the path= πR²-πr²

where, R= 28/2m+ 1.75m= 14m+1.75m= 15.75m

and r= 28m/2= 14

Area= π(R²-r²)

= 22/7( 15.75m+14m)(15.75m-14m)

= 22/7 ( 29.75m)(1.75m)

= 22×4.25m×1.75m

=163.625m²

cost of gravelling= 163.625m²×5/m² = 818.125