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

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*\frac {22}{7}×r=330`

`\qquad \quad{:}\longmapsto\tt \frac {44}{7}r=330`

`\qquad \quad{:}\longmapsto\tt r=\frac {330×7 }{44}`

`\qquad \quad{:}\longmapsto\tt r=(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=(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 \frac {22}{7}(60)^2`

`\qquad \quad{:}\longmapsto\tt \frac {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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