Question

the inner circumference of a circular track is 264 m and the width of the track is 7 m. find :

(1) the radius of the outer circumference.
(2) the length of the outer circumferenc.
(3) the cost of fencing the outer circumference at the rate of rupees 50 per m.

please answers in full.

Answer 1

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Answer 2

Answer:

Circumference of a circle(C) is given by:

$C =2 \pi r$

where r is the radius of the circle

As per the statement:

the inner circumference of a circular track is 264 m and the width of the track is 7 m.

See the diagram as shown below:

(1)

Circumference of a inner circular track(C') is given by:

$C' =2 \pi r'$

where r' is the inner radius of the circular track.

Substitute the given values we have;

Use value of $\pi = \frac{22}{7}$

$264=2 \frac{22}{7} \cdot r'$

$264=\frac{44}{7} \cdot r'$

Divide both sides by 44 we have;

$6=\frac{1}{7} \cdot r'$

Multiply both sides by 7 we get;

42 m=r'

or

r' = 42 m

Since, the width of the circular track is 7 m

Then;

Radius of the outer circular track(R) = r'+7 = 42+7 = 49 m

(2)

Length of the outer circumference(C") is given by:

$C"= 2 \pi R$

Substitute the value of R we have;

$C'' = 2 \cdot \frac{22}{7} \cdot 49 = 44 \cdot 7 = 308 m$

Therefore, the length of the outer circumference is 308 m.

(3)

Find the cost of fencing the outer circumference at the rate of rupees 50 per m.

In 1 m = Rs 50

then;

In 308 m = $308 \cdot 50 = Rs. 15,400$

Therefore, cost of fencing the outer circumference at the rate of rupees 50 per m is Rs. 15,400