Question

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

Answer 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

Answer 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.