Question

The area between two eccentric circles is 1078cm2. The circumference of the inner circle is 132cm.

Calculate the radius of the outer circle​

Answer 1

Answer:

$\bigstar{\bold{Radius\:of\:outer\:circle=28\:cm}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Area between two concentric circles = 1078 cm²
• Circumference of the inner circle = 132 cm

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Radius of the outer circle

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the radius of the inner circle

→ Perimeter of a circle is given by the formula,

  Perimeter of a circle = 2 π r

→ Hence

  Perimeter of inner circle = 2 × 3.14 × r

  132 = 2 × 3.14 × r

  r = 132/6.28

  r = 21 cm

→ Hence the radius of the inner circle is 21 cm

→ Now we have to find the area of the inner circle

→ Area of a circle is given by

  Area of a circle = π r²

→ Substituting the datas we get,

  Area of inner circle = 3.14 × 21 × 21

  Area of inner circle = 1384.74 cm²

→ Now,

  The area of outer circle = Area of inner circle + Area between the circles

→ Hence,

  Area of outer circle = 1384.74 + 1078

  Area of outer circle = 2462.74 cm²

→ Now,

  π R² = 2462.74

→ Solving it we get the value of R

   R² = 2462.74/3.14

   R² = 784.3

   R = √784.3

   R = 28 cm

→ Hence radius of the outer circle is 28 cm

$\boxed{\bold{Radius\:of\:outer\:circle=28\:cm}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The perimeter of a circle is given by

   Perimeter of a circle = 2 π r

→ Area of a circle is given by

  Area of a circle = π r²

Answer 2

ᎯᏁᏕᏯᎬᏒ

⋆ Circumference of inner circle = 2πr

$\boxed{2πr = 132~cm} \\ </p><p>$

$r =132 \times \frac{7}{22 \times 2}$

$∴~\red{r = 21cm}$

⋆ Area of inner circle = πr²

⋆ Area of outer circle = πR²

$\boxed{πR² - πr² = 1078 ~cm²}$

$π(R²-r²) = 1078$

$R² - r² = 1078 \times \frac{7 }{22}$

$R² -( 21)² = 343$

$R² - 441 = 343$

$R² = 441 + 343$

$R² = 784$

$R = \sqrt{784}$

$\red{R = 28 \: cm}$

$\therefore~\underline{ \sf{ Radius \: of \: outer \: circle = 28 \: cm}}$