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

14 Likes

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.

Answered By

8 Likes

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

Related Questions

The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km/hr. Give your answer, correct to the nearest km.

The circumference of a circle is 123.2 cm. Calculate :
(i) the radius of the circle in cm.
(ii) the area of the circle in cm², correct to nearest cm².
(iii) the effect on the area of the circle if the radius is doubled.

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹50 per m².

In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.

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

Related Questions

The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km/hr. Give your answer, correct to the nearest km.

The circumference of a circle is 123.2 cm. Calculate :(i) the radius of the circle in cm.(ii) the area of the circle in cm2, correct to nearest cm2.(iii) the effect on the area of the circle if the radius is doubled.

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹50 per m2.

In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm2. The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.

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.

The circumference of a circle is 123.2 cm. Calculate :
(i) the radius of the circle in cm.
(ii) the area of the circle in cm², correct to nearest cm².
(iii) the effect on the area of the circle if the radius is doubled.

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹50 per m².

In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.