In the figure (i) given below, the area enclosed between the concentric circles is 770 cm 2 . Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

Let radius of inner circle = r cm. From figure, Area of shaded region = Area of outer circle - Area of inner circle ⇒ 770 = π(21) 2 - πr 2 ⇒ 770 = 441π - πr 2 ⇒ 770 = π(441 - r 2 ) ⇒ 441 - r 2 = ⇒ 441 - r 2 = ⇒ 441 - r 2 = ⇒ 441 - r 2 = 245 ⇒ r 2 = 441 - 245 ⇒ r 2 = 196 ⇒ r = = 14 cm. Hence, radius of inner circle = 14 cm.

Mathematics

In the figure (i) given below, the area enclosed between the concentric circles is 770 cm². Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

Mensuration

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Answer

Let radius of inner circle = r cm.

From figure,

Area of shaded region = Area of outer circle - Area of inner circle

⇒ 770 = π(21)² - πr²

⇒ 770 = 441π - πr²

⇒ 770 = π(441 - r²)

⇒ 441 - r² = $\dfrac{770}{π}$

⇒ 441 - r² = $\dfrac{770}{\dfrac{22}{7}}$

⇒ 441 - r² = $\dfrac{770 \times 7}{22}$

⇒ 441 - r² = 245

⇒ r² = 441 - 245

⇒ r² = 196

⇒ r = $\sqrt{196}$ = 14 cm.

Hence, radius of inner circle = 14 cm.

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Mathematics

In the figure (i) given below, the area enclosed between the concentric circles is 770 cm². Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

Mensuration

Answer

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In the figure (i) given below, the area enclosed between the concentric circles is 770 cm2. Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

Mensuration

Answer

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