Question

The inner circumference of a circular track is 440 metre and the track is 14 m wide. Find how much larger is outer track than the inner?

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Perimeter of Circle has been used. We know that the radius of smaller track in addition to the width is the radius of outer track. And hence, we can find out the difference.

Let's do it !!

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★ Formula Used :-

$\: \: \boxed{\boxed{\bf{Circumference \: of \: Circle \: = \: 2 \: \times \: \pi r}}}$

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★ Question :-

The inner circumference of a circular track is 440 metre and the track is 14 m wide. Find how much larger is outer track than the inner?

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★ Solution :-

» Circumference of Inner Track = 440 m

» Width of outer track than inner = 14 m

• Let the radius of the inner track be 'r' m

• Let the radius of outer track be '(r + 14)' m

~ Note* : here we are using π = 22/7

Then, according to the question :-

✒ Circumference of Circle (inner) = 2πr

✒ 2πr = 440

$\: \large{\bf{\longmapsto \: \: r \: = \: \dfrac{440\: × \: 7}{22 \: \times \: 2}}}$

✒ r = 10 × 7

$\: \large{\boxed{\boxed{\rm{r \: = \: 70 \: m}}}}$

Hence, the radius of inner track = r = 70 m

• Then, radius of outer track = r + 14 = 70 + 14

= 84 m

Then, circumference of outer track is :-

✒ Circumference of outer track = 2π × radius

✒ Circumference of outer track = 2 × (22/7) × 84

✒ Circumference of Outer Track = 2 × 22 × 12

$\: \: \underbrace{\large{\bf{Circumference \: of \: outer \: track \: = \: 528 \: m}}}$

Now the difference of between the track is given as :-

=> Difference = 528 - 440 = 88 m

• So the larger track is 88 m longer than the shorter track.

$\: \: \\ \: \boxed{\rm{\leadsto \: \: Hence, \: the \: outer \: track \: is \: longer \: than \: inner \: track \: by \: \underline{\boxed{\underline{88 \: m}}}}}$

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$\large{\underbrace{\underline{\tt{\leadsto \: \: Reference \: as \: Supplementary \: Counsel \: :-}}}}$

• Area of Circle : πr²

• Area of Square : (Side)²

• Area of Rectangle : Length × Breadth

• Area of Triangle : ½ × Base × Height

• Perimeter of Rectangle : 2(Length + Breadth)

• Perimeter of Square : 4 × Side

• Perimeter of Triangle : Sum of all sides

• Area of Parallelogram : Base × Height

Answer 2

Answer:-

Given:

Inner circumference of a circular track = 440 m

Width of the track = 14 m.

Let the radius of the radius of the inner track be r m.

So, radius of the outer track = (r + 14) m.

We know that,

Circumference of a circle = 2πr.

So,

⟶ 2 * (22/7) * r = 440

⟶ r = 440 * (1/2) * (7/22)

⟶ r = 70 m

Hence,

• Radius of the track (r) = 70 m.

Now,

We have to find the difference between the outer circumference and the inner Circumference of the track.

⟶ Difference = 2π(r + 14) - 2πr

⟶ Difference = 2 * (22/7) * (70 + 14) - 440

⟶ Difference = 44 * 84/7 - 440

⟶ Difference = 528 - 440

⟶ Difference = 88 m

∴ The outer circumference is 88 m larger than the inner Circumference.