Question

a circular pond has a 90 cm wide footpath along its edge. A man walks around the outer edge of footpath with 66 cm long steps.In 400 steps he makes a full round.What is the radius of the pon d?

Answer 1

Answers to the question is 4110 cm
Please refer the above photograph for the used process.

Answer 2

The radius of the pond is 4110 cm or 41.1 metre.

Given:

• A circular pond has a 90 cm wide footpath along its edge.
• A man walks around the outer edge of the footpath with 66 cm long steps.
• In 400 steps he makes a full round.

To find:

• What is the radius of the pond?

Solution:

Formula to be used:

Circumference of circle= $\bf 2\pi \: r$

Step 1:

Find the circumference of the outer edge of the path.

Circumference of path's outer edge$= 66 \times 400 \: cm$

Step 2:

Find the radius of path and pond. (Both inclusive)

$2\pi \: R = 66 \times 400$

$R = \frac{66 \times 400 \times 7}{2 \times 22}$

$\bf R = 4200 \: cm$

See attachment, here we can say that AB is 4200 cm.

Step 3:

Find the radius of the pond.

ATQ, the width of path is 90 cm.

So,

Radius of pond : CB= AB-AC

$r = 4200 - 90$

$\bf r = 4110 \: cm$

Thus,

Radius of pond is 4110 cm or 41.1 metre.

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