Question

A skating champion moves along the circumference of a circle of radius 21 meters in 44 seconds. How many
seconds will it take her to move along the perimeter of a hexagon of side 42 meters?​

Answer 1

Given,

The radius of the circle$\[ = 21{\rm{m}}\]$

The time is taken to cover the distance$\[ = 44\sec \]$

The length of a side of hexagon$\[ = 42{\rm{m}}\]$

Solution,

The perimeter of a circle is

$\[\begin{array}{l} = 2 \times \frac{{22}}{7} \times 21\\ = 2 \times 22 \times 3\\ = 22 \times 6\\ = 132\end{array}\]$

The speed of the skater to cover the circular path

$\[\begin{array}{l} = \frac{{132}}{{44}}\\ = 3{\rm{m/s}}\end{array}\]$

The perimeter of the hexagon is

$\[\begin{array}{l} = 6 \times 48\\ = 288{\rm{m}}\end{array}\]$

Therefore, the time taken to cover the hexagonal path is

$\[\begin{array}{l} = \frac{{288}}{3}\sec \\ = 96\sec \end{array}\]$

Hence, the time taken to cover the hexagonal path is $\[96\]$sec.

Answer 2

Answer:

Time required to travel along the perimeter of a hexagon  = 84seconds

Step-by-step explanation:

Given,

The radius of the circle = 21m

Time taken to travel the circumference of the circle = 44seconds

Side of a hexagon = 42m

To find,

The time taken to move along the perimeter of a hexagon.

Recall the concept

Circumference of the circle =2πr

The perimeter of a hexagon = 6× length of a side

Distance = speed × time

Solution

Since the radius of the circle = 21m,

The circumference of the circle = 2× $\frac{22}{7}$×21 = 132m

Since time taken to travel 132 m is 44seconds

Speed = $\frac{distance }{time}$ = $\frac{132}{44}$ = 3m/s

Since the length of a side of a hexagon = 42m,

the perimeter of a hexagon = 6×42 = 252m

Time required to travel along the perimeter of a hexagon = $\frac{distance }{speed}$

= $\frac{252}{3}$ = 84seconds

∴ Time required to travel along the perimeter of a hexagon = 84seconds

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