Question

The outer edge of a circular running track is 330m long. If it is widened by 7m all around, find the cost of widening it at 8 per square metre.​

Answer 1

Answer:

Here given that perimeter of circular running track =330m

Let radius=r

As we know that in a circle

${\boxed{\sf Perimeter=2\pi r}}$

• Substitute the values

$\qquad \quad{:}\longmapsto\tt 2\times\dfrac {22}{7}×r=330$

$\qquad \quad{:}\longmapsto\tt \dfrac {44}{7}r=330$

$\qquad \quad{:}\longmapsto\tt r=\dfrac {330×7 }{44}$

$\qquad \quad{:}\longmapsto\tt r=\dfrac{2310}{44}$

$\qquad \quad{:}\longmapsto\tt r=52.5$

$\therefore\sf r=53m (Approx)$

Again

${\boxed{\sf Area=\pi r^2 }}$

• Substitute the values

$\qquad \quad{:}\longmapsto\tt Area=\dfrac{22}{7}×(53)^2$

$\qquad \quad{:}\longmapsto\tt Area=8828.2m^2$

$\therefore\sf Area=8828m^2 (Approx)$

Now

the radius is increased by 7m

Hence

New radius=(x+7)m=53+7=60m

New Area=

$\qquad \quad{:}\longmapsto\tt \pi. r^2$

$\qquad \quad{:}\longmapsto\tt \dfrac {22}{7}(60)^2$

$\qquad \quad{:}\longmapsto\tt \dfrac {22}{7}×3600$

$\qquad \quad{:}\longmapsto\tt 11314.28m^2$

$\therefore\sf AREA=11314m^2 (Approx).$

now

Area of widened Area=New area-Old Area

$\qquad \quad{:}\longmapsto\tt 11314-8828$

$\qquad \quad{:}\longmapsto\tt 2486m^2$

• Cost of widening per square=8

Total cost=

$\qquad \quad{:}\longmapsto\tt 2486×8$

$\qquad \quad{:}\longmapsto\tt 19888$

$\therefore\sf Total\:cost\:is\: 19888.$

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