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There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 66 cm long and he takes exactly 400 steps to go around the pond, find the diameter of the pond.

Solution:

If the person takes 400 steps to go around the pond and

Each step covers 66cm distance

Therefore total distance covered by taking one round of the circular pond by the person = 66 × 400 = 26400cm = 264 m

Therefore circumference of the circular pond = 264 m

Circumference of the circular pond = 2πr = πd where d = diameter of the pond = 2r

Therefore,

πd = 264

(22/7)d = 264

d = (264/22) × 7

d = 12 × 7 = 84 m

Hence the diameter of th circular pond is 84m

✦ Try This: There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 55 cm long and he takes exactly 600 steps to go around the pond, find the diameter of the pond.

If the person takes 600 steps to go around the pond and

Each step covers 55cm distance

Therefore total distance covered by taking one round of the circular pond by the person = 55 × 600 = 33000cm = 330 m

Therefore circumference of the circular pond = 330 m

Circumference of the circular pond = 2πr = πd where d = diameter of the pond = 2r

Therefore,

πd = 330

(22/7)d = 330

d = (330/22) × 7

d = (30/2) × 7

d = 15 × 7 m

d = 105 m

Hence the diameter of th circular pond is 105m

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 70

There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 66 cm long and he takes exactly 400 steps to go around the pond, find the diameter of the pond.

Summary:

There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 66 cm long and he takes exactly 400 steps to go around the pond, the diameter of the pond is 84m

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