A path of width 3.5 m runs around a semi­circular grassy plot whose perimeter is 72 m. Find the area of the path.

Asked by Sakshi | 9 months ago |  152

1 Answer

Solution :-

Perimeter of semicircle grassy plot = 72 m
RD Sharma Mathematics Class 10 Pdf Download Free Chapter 15 Areas related to Circles
Let r be the radius of the plot

Perimeter of semi-circle = 72 m 

Width of path around it = 3.5 m 

Perimeter of semi-circle = πr + 2r 

=  \( \dfrac{22}{7}+r+2r=72\)

= 22r + 14r = 72 × 7 

= r = 14 cm

Radius including the width of path(R)

= r + 3.5 = 14 + 3.5 = 17.5 m  

So, 

area of path =\( \dfrac{\pi}{2}((17.5)^2-(14)^2)\)

= 173.25m2

Answered by Sakshi | 9 months ago

Related Questions

Prove that the area of a circular path of uniform width hsurrounding a circular region of radius r is πh(2r + h).
 

Class 10 Maths Areas Related to Circles View Answer

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.
 

Class 10 Maths Areas Related to Circles View Answer

The outer circumference of a circular race-track is 528 m. The track is every­where 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre 
 

Class 10 Maths Areas Related to Circles View Answer

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14)

Class 10 Maths Areas Related to Circles View Answer

Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle, such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place.

Class 10 Maths Areas Related to Circles View Answer