Question

A race track is in the form of a ring whose outer circumference is 44om and width of the track 7m . Find the area of the track

Answer 1

Correct Question :-

A race track is in the form of a ring whose outer circumference is 440 m and width of the track 7 m. Find the area of the track.

Concept :-

• In the above question, we are asked to find the the area of the race track, which can be easily found out by calculating the radius of inner circle by applying simple formulas.

Formulas used :-

• circumference of circle = 2πr

• area of ring = π (R²-r²)

Solution :-

• Let the radius of the outer circle be R and

• the radius of inner circle be r

According to the Question :-

⇒ Circumference of outer circle = 440 m

⇒ 2πR = 440 m

⇒ πR = $\large{\mathtt{\frac{440\:m}{2}}}$

⇒ $\large{\mathtt{\frac{22}{7}R=220\:m}}$

⇒$\large{\mathtt{R=\frac{220\:m×7}{22}}}$

∴ R = 70 m

we know :-

⇒ R = (r) + (width of the track)

⇒ 70 m = r + 7 m

⇒ r = 70 m - 7 m

∴ r = 63 m

As we know :-

⇒ Area of a ring = π(R²-r²)

⇒ Area of a ring = π{(70)²-(63)²}

⇒ Area of a ring = $\large{\mathtt{\frac{22}{7}×931}}$

∴ Area of the ring is 2926 m²

Know More :-

• Diameter = 2×Radius

• Circumference of circle = 2πr

• Area of circle = πr²

• Circumference of semicircle = r (π+2)

• Area of semicircle = ½×πr²

• Circumference of Quadrant = r (½π + 2)

• Area of quadrant = ¼×πr²

• Area of sector = $\large{\mathtt{\frac{Θ×πr²}{360}}}$

Answer 2

Answer:$\frac{0 \times {\pi}^{2} }{360}$

Formula:

• circumference of circle = 2πr

• area of ring = π (R²-r²)

Solution :

• Let the radius of the outer circle be R and

• the radius of inner circle be r

According to the Question :

→ Circumference of outer circle = 440 m

→ 2πR= 440 m

$\pi \: R= \frac{440m}{2}$

$→\frac{22}{7} R = 220m$

$→R = \frac{220m \times 7}{22}$

• R = 70 m

we know that :

R = (r) + (width of the track)

→ 70 m = r + 7m

⇒ r = 70 m-7m

→r = 63 m

we know that :

→ Area of a ring = π(R²-r²)

→ Area of a ring = π(70)²-(63)²

Area of a ring = $\frac{22}{7} \times 931$

Area of the ring is 2926 m²

Know More :

• Diameter = 2×Radius

• Circumference of circle = 2πr

• Area of circle = πr²

• Circumference of semicircle =r(π+2)

• Area of semicircle = $\frac{1}{2} \times \pi \: {r}^{2}$

• Circumference of Quadrant = $r( \frac{1}{2} \pi + 2)$

• Area of quadrant = $\frac{1}{4}\times {\pi}^{2}$

• Area of sector =$\frac{0\times {\pi}^{2} }{360}$