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

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

KnowledgeBoat · Accepted Answer

Let radius of inner circle be r cm.

Given,

Area enclosed between two concentric circles is 770 cm²

Area enclosed between two concentric circles = Area of bigger circle - Area of smaller circle

⇒ 770 = π(21)² - πr²

⇒ 770 = 441π - πr²

⇒ 770 = $\dfrac{22}{7}$ (441 - r²)

⇒ 441 - r² = $\dfrac{770 × 7}{22}$

⇒ 441 - r² = 35 × 7

⇒ 441 - r² = 245

⇒ r² = 441 - 245

⇒ r² = 196

⇒ r = $\sqrt{196}$ = 14 cm.

Hence, radius of inner circle = 14 cm.

Mathematics