Question

The area enclosed between two concentric circle is 770 cm². if diameter of outer circle is 42 cm . find radius , diameter, circumference of inner circle ​

Answer 1

Answer:-

Given:-

The area enclosed between two concentric circles = 770 cm².

That means ,

Area of the larger circle - Area of the smaller circle = 770 cm².

Also given that,

Diameter of bigger circle = 42 cm.

⟶ radius = 42/2 = 21 cm.

We know that,

Area of a circle = πr²

(Where r is the radius).

Let the radius of smaller circle be r cm.

According to the question,

⟹ π(21)² - πr² = 770

⟹ π (441 - r²) = 770

⟹ 441 - r² = 770 × 7/22

[ π = 22/7 ]

⟹ 441 - r² = 245

⟹ 441 - 245 = r²

⟹ 196 = r²

⟹ (14)² = r²

⟹ r = 14 cm.

Now,

Diameter of the inner circle = 2(14) = 28 cm.

We know,

Circumference of a circle = 2πr

⟶ Circumference of the circle = 2(22/7)(14) = 22 × 2 × 2 = 88 cm.

Answer 2

$\mathbb{\huge{\underline{Question\: :-}}}$

• The area enclosed between two concentric circles is 770 cm². If diameter of outer circle is 42 cm , Find radius , diameter, circumference of inner circle.

Given :-

• The area enclosed between two concentric circles is 770 cm²

• Diameter of outer circle = 42 cm

$\mathbb{\huge{\underline{AnsweR \: :-}}}$

The area enclosed between the circles is 770 cm² so we can write it as ,

Area of large circle - Area of smaller circle = 770 ----(i)

And ,

• Diameter = 42 cm

We know that :-

• Radius = Diameter/2

• Radius (R) = 42/2

• So radius of larger circle (R) = 21 Cm

Using the identity →

• $\sf \: area \: of \: a \: circle = \pi {r}^{2}$

Let the Radius of smaller circle is r cm , So according to the equation (i) →

$\star\sf \: area \: of \: larger \: circle - area \: of \: small \: circle = 770 \: {cm}^{2} \\ \\ \implies \sf \: \pi {(21)}^{2} - \pi {r}^{2} = 770 \\ \\ \sf \: taking \: \pi \: common \longrightarrow \\ \\ \implies \sf \: \pi( {21}^{2} - {r}^{2} ) = 770 \\ \\ \implies \sf \: \pi(441 - {r}^{2} ) = 770 \\ \\ \sf \: we \: know \: that \: \pi = \frac{22}{7} \\ \\ \implies \sf \frac{22}{7} (441 - {r}^{2} ) = 770 \\ \\ \implies \sf441 - {r}^{2} = 770 \times \frac{7}{22} \\ \\ \implies \sf441 - {r}^{2} = 35 \times 7 \\ \\ \implies \sf441 - {r}^{2} = 245 \\ \\ \implies \sf {r}^{2} = 441 - 245 \\ \\ \implies \sf {r}^{2} = 196 \\ \\ \implies \sf \: r = \sqrt{196} \\ \\ \implies \boxed{ \sf \: r = 14 \: cm}$

Hence, the radius of smaller circle is 14.

So, the diameter of inner circle = 2 × r

= 2 × 14

= 28 CM

$\star \sf \: and \: circumference \: of \: smaller \: circle = 2\pi r \\ \\ \sf \: = 2 \times \frac{22}{7} \times 14 \\ \\ \sf \: = 2 \times 22 \times 2 \\ \\ \sf = 88 \: {cm}^{2} \\ \\ \boxed{ \star \sf circumference \: of \: circle = 88 \: {cm}^{2} }$

Hence, the radius of circle is 14 cm , diameter of circle is 28 cm and Circumference is 88 cm².

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Hope it will help you :)