the area between a concentric circle is 1540cm². If the radius of the outer circle is 21 cm, calculate the radius of the inner cir

2 thoughts on “the area between a concentric circle is 1540cm². If the radius of the outer circle is 21 cm, calculate the radius of the inner cir”

1. Correct Question:

   The area enclosed between the concentric circles is 770 cm². If the radius of the outer circle is 21 cm, find the radius of the inner circle.

   Answer:

   The radius of the inner circle is 14 cm.

   Step-by-step explanation:

   Given that:

   The area between a concentric circle is 770 cm².

   The radius of the outer circle is 21 cm.

   To Find:

   The radius of the inner circle.

   Let us assume:

   The radius of the inner circle be x.

   Formula:

   Area between a concentric circle = π(R² – r²)

   Where,

   R = The radius of the outer circle

   r = The radius of the inner circle

   Finding the radius of the inner circle:

   According to the question.

   ⟶ π(21² – x²) = 770

   ⟶ π(441 – x²) = 770

   ⟶ 441 – x² = 770/π

   ⟶ 441 – x² = (770 × 7)/22

   ⟶ 441 – x² = 245

   ⟶ x² = 441 – 245

   ⟶ x² = 196

   ⟶ x = √196

   ⟶ x = 14

   ∴ The radius of the inner circle = 14 cm

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2. Let the radius of inner circle be r.

   Area enclosed between two concentric circles

   ⇒ π[(21)2 – (r)2] = 770

   ⇒ (21)2 – (r)2 = 770/π = 770 × 7/22

   = 35 × 7

   ⇒ (21)2 – (r)2 = 245

   ⇒ 441 – r2 = 245

   ⇒ 441 – 245 = r2

   ⇒ 196 = r2

   ⇒ 14 = r

   The radius of inner circle = 14 cm.

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