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The inner circumference of a circular track is 440 cm. The track is 14 cm wide. Find the diameterof the outer circle of the track.
- a)84 cm
- b)168 cm
- c)336 cm
- d)77 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The inner circumference of a circular track is 440 cm. The track is 14...
Let inner radius = A; then 2pr = 440 \ p = 70
Radius of outer circle = 70 + 14 = 84 cm
Outer diameter = 2 × Radius = 2 × 84 = 168
Radius of outer circle = 70 + 14 = 84 cm
Outer diameter = 2 × Radius = 2 × 84 = 168
Most Upvoted Answer
The inner circumference of a circular track is 440 cm. The track is 14...
Given, Inner circumference of the circular track = 440 cm
Width of the track = 14 cm
Let the diameter of the outer circle be 'd' cm
So, the diameter of the inner circle will be (d - 2 × 14) cm
We know that,
Circumference of a circle = π × Diameter
Inner circumference = π × (d - 2 × 14) cm
Outer circumference = π × d cm
As the track is formed by the outer and inner circles, the total width of the track will be the difference between the outer and inner circumferences.
So, the width of the track = Outer circumference - Inner circumference
14 cm = πd - π(d - 28)
14 cm = πd - πd + 28π
28π = 14 cm
π = 0.5 cm
Substituting the value of π in the equations of inner and outer circumferences, we get:
440 = 0.5 × (d - 28)
d - 28 = 880
d = 908
Therefore, the diameter of the outer circle of the track is 908 cm.
Hence, the correct option is (b) 168 cm.
Width of the track = 14 cm
Let the diameter of the outer circle be 'd' cm
So, the diameter of the inner circle will be (d - 2 × 14) cm
We know that,
Circumference of a circle = π × Diameter
Inner circumference = π × (d - 2 × 14) cm
Outer circumference = π × d cm
As the track is formed by the outer and inner circles, the total width of the track will be the difference between the outer and inner circumferences.
So, the width of the track = Outer circumference - Inner circumference
14 cm = πd - π(d - 28)
14 cm = πd - πd + 28π
28π = 14 cm
π = 0.5 cm
Substituting the value of π in the equations of inner and outer circumferences, we get:
440 = 0.5 × (d - 28)
d - 28 = 880
d = 908
Therefore, the diameter of the outer circle of the track is 908 cm.
Hence, the correct option is (b) 168 cm.
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