Question

A track is in the form of a ring whose inner and outer circumference are 88m and 132m , respectively . Find the width of the track and also the annulus.
I will mark you as a brainlest if a proper answer.
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Answer 1

Answer:

Outer Circumference = 132 cm

=> Radius = Circumference / 2π

=> Radius = 132 / (2 × 22/7)

=> Radius = 132 / (44/7)

=> Radius = 132 × 7/44

=> Radius = 3 × 7

=> Radius = 21 cm

Inner Circumference = 88 cm

=> Radius = Circumference / 2π

=> Radius = 88 / (2 × 22/7)

=> Radius = 88 / (44/7)

=> Radius = 88 × 7/44

=> Radius = 2 × 7

=> Radius = 14 cm

Width of the ring = Outer Radius - Inner radius

= 21 - 14

= 7cm

Answer 2

Answer:

$\bigstar{\bold{Annulus=770\:m^{2}}}$

$\bigstar{\bold{Width\:of\:the\:track=7\:m}}$

Step-by-step explanation:

$\Large{\underline{\underline{\sf{Given:}}}}$

• Outer circumference = 132 m
• Innner circumfurence = 88 m

$\Large{\underline{\underline{\sf{To\:Find:}}}}$

• Width of the track
• Annulus

$\Large{\underline{\underline{\sf{Solution:}}}}$

➠ Here let us find the annulus or the area of the track

➠ First let us find the radius of the outer and inner circles.

➠ The perimeter of a circle is given by,

     Perimeter of a circle = 2 π r

➠ Substituting the value for perimeter,

➠ Perimeter of inner circle = 2 π r

    88 = 2 × 3.14 × r

    r = 88/6.28

    r = 14 m

➠ Perimeter of outer circle = 2 π R

    132 = 2 × 3.14 × R

    R = 132/6.28

    R = 21 m

➠ Now we have to find the area of the outer and inner circles

➠ Area of a circle is given by,

   Area of a circle = π r²

➠ Area of outer circle = 22/7 × 21 × 21

    Area of outer circle = 22 × 3 × 21

    Area of outer circle = 1386 m²

➠ Now finding the area of inner circle

    Area of inner circle =  π r²

    Area of inner circle =  22/7 × 14 × 14

    Area of inner circle = 22 × 2 × 14

    Area of inner circle = 616 m²

➠ Now the annulus or area of the track is given by,

    Area of track = Area of outer circle - Area of inner circle

➠ Substitute the data,

    Area of track = 1386 - 616

    Area of track = 770 m²

➠ Hence the annulus is 770 m²

    $\boxed{\bold{Annulus=770\:m^{2}}}$

➠ Now we have to find the width of the track

➠ Width of the track = Outer radius - Inner radius

➠ Substitute the data,

    Width of the track = 21 - 14

    Width of the track = 7 m

➠ Hence width of the track is 7 m

    $\boxed{\bold{Width\:of\:the\:track=7\:m}}$

$\Large{\underline{\underline{\sf{Notes:}}}}$

➠ Perimeter of a circle is given by

    Perimeter of a circle = 2 π r or π d

➠ Area of a circle is given by,

    Area of a circle = π r²