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.
Answers
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.
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