Question

A circular path runs around a circular flower bed if the circumference of the flower bed and path are 88 m and 132 m respectively, find the width of the path also find the area of path

Answer 1

GIVEN:

Circumference of the flower bed (inner circumference)= 88 cm

Circumference of the path (outer circumference)= 132

Let the outer and inner radii be R & r

Circumference of the circle= 2π r

Outer Circumference of a circle= 2πR

132 = 2× (22/7)×R

R= 132×( 7/22)(1/2)= (66×7)/22= 3×7= 21cm

Inner circumference of a circle= 2πr

88 = 2× (22/7)×r

r= 88×(7/22)×(1/2)= (4×7)/2= 2×7= 14cm

Width of a track =( R-r)= 21-14= 7 cm


Area of a circle= πr²

Area of outer circle= πR²= 22/7×(21)²

=( 22/7)× 21×21

= 22×3×21

=66×21

=1386 cm²

Area of outer circle= 1386 cm²

Area of inner circle= πr²

=( 22/7)× 14²

=( 22/7)×14×14

= 22×2× 14

=44×14= 616cm²

Area of inner circle= 616 cm²

Area of path= area of outer circle - area of inner circle

Area of path= 1386 - 616 = 770 cm²

Hence the width of a path is 7 cm an area of path is 770 cm²

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