Class 10 Maths Areas Related to Circles questions with solutions

Q 1 :

The area of a quadrant of a circle, whose circumference is 22 cm, is

$\frac{11}{8} c m^{2}$
$\frac{77}{8} c m^{2}$
$\frac{77}{2} c m^{2}$
$\frac{77}{4} c m^{2}$

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(2) $\frac{77}{8} c m^{2}$

Q 2 :

The number of revolutions made by a circular wheel of radius 0.25m in rolling a distance of 11km is

2800
4000
5500
7000

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(4)

Since, radius of wheel $(r) = 0.25 m$

Total distance covered by a circular wheel = 11 km = 11000 m

$\Rightarrow No. of revolutions \times 2 π r = 11000$

$\Rightarrow No. of revolutions = \frac{11000 \times 7}{2 \times 22 \times 0.25} = 7000$

Q 3 :

If the length of an arc of a circle subtending an angle $60 °$ at its centre is 22 cm, then the radius of the circle is :

$\sqrt{21}$ cm
$21$ cm
$\sqrt{42}$ cm
$42$ cm

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(2) 21 cm

Q 4 :

The diagonals of a rhombus ABCD intersect at O. Taking ‘O’ as the centre, an arc of radius 6 cm is drawn intersecting OA and OD at E and F respectively. The area of the sector OEF is :

$9 π$ ${cm}^{2}$
$3 π$ ${cm}^{2}$
$12 π$ ${cm}^{2}$
$18 π$ ${cm}^{2}$

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(1) $9 π$ ${cm}^{2}$

Q 5 :

If the sum of the areas of two circles with radii $R_{1} a n d R_{2}$ is equal to the area of a circle of radius R , then:

$R_{1} + R_{2} = R$
$R_{1}^{2} + R_{2}^{2} = R^{2}$
$R_{1} + R_{2} < R$
$R_{1}^{2} + R_{2}^{2} < R^{2}$

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(2)

According to the question,

$π R_{1}^{2} + π R_{2}^{2} = π R^{2} \Rightarrow π (R_{1}^{2} + R_{2}^{2}) = π R^{2} \Rightarrow R_{1}^{2} + R_{2}^{2} = R^{2}$

Q 6 :

The area of the circle that can be inscribed in a square of side 6 cm is:

$36 π {cm}^{2}$
$18 π {cm}^{2}$
$12 π {cm}^{2}$
$9 π {cm}^{2}$

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(4)

Let a circle with centre at O, having radius r, is inscribed in a square of side 6 cm as shown in Fig.

$D i a m e t e r o f t h e c i r c l e = 6 c m \Rightarrow 2 r = 6 \Rightarrow r = 3 cm Area of circle = {πr}^{2} = π \times (3)^{2} = 9 π {cm}^{2}$

Q 7 :

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is:

$22 : 7$
$14 : 11$
$7 : 22$
$11 : 14$

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(2)

Let r be the radius of the circle and x be the length of each side of the square.

According to the question, Perimeter of circle = Perimeter of square

$2 π r = 4 x \Rightarrow π r = 2 x \Rightarrow r = \frac{2 x}{π} (i) \Rightarrow \frac{Area of circle}{Area of square} = \frac{π r^{2}}{x^{2}} = \frac{π \times \frac{4 x^{2}}{π^{2}}}{x^{2}} = \frac{4}{π} \Rightarrow \frac{Area of circle}{Area of square} = \frac{4}{\frac{22}{7}} = \frac{4}{\frac{22}{7}} \times 7 = \frac{28}{22} = \frac{14}{11} R e q u i r e d r a t i o i s 14 : 11$

Q 8 :

If the area of a circle is $64 π c m^{2}$ then its circumference is:

$7 π cm$
$16 π cm$
$14 π cm$
$21 π cm$

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Let r be the radius of the circle. Then,

$π r^{2} = 64 π \Rightarrow r^{2} = 64 \Rightarrow r = 8 cm Circumference of the circle = 2 πr = 2 π \times 8 cm = 16 π cm$

Q 9 :

If the areas of two circles are in the ratio 4:9, then the ratio of their perimeters of their semi-circles is:

2:3
$3 : 2$
$1 : 2$
$1 : 3$

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(1)

Let the radii of two circles be $r_{1} a n d r_{2}$ . It is given that

$π r_{1}^{2} : π r_{2}^{2} = 4 : 9 \Rightarrow r_{1}^{2} : r_{2}^{2} = 4 : 9 \Rightarrow r_{1} : r_{2} = 2 : 3 L e t P_{1} a n d P_{2} b e t h e p e r i m e t e r s o f t h e t w o s e m i - c i r c l e s . T h e n, P_{1} = π r_{1} + 2 r_{1} P_{2} = π r_{2} + 2 r_{2} \Rightarrow P_{1} = (π + 2) r_{1} and P_{2} = (π + 2) r_{2} \Rightarrow P_{1} : P_{2} = r_{1} : r_{2} = 2 : 3$

Q 10 :

Which of the following statements are true regarding a circle of radius ‘R’?

$(i) A r e a o f c i r c l e = π R^{2} (i i) C i r c u m f e r e n c e o f c i r c l e = π R (i i i) \frac{Area of circle}{Circumference of circle} = \frac{R}{2} (i v) A r e a o f c i r c l e i s a l w a y s g r e a t e r t h a n i t s c i r c u m f e r e n c e$

Choose the correct option from the following:

(i) and (iii)
(ii) and (iii)
(iii) and (iv)
(i) and (iv)

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(1)

$A r e a o f c i r c l e o f r a d i u s R = π R^{2} ∴ S t a t e m e n t (i) i s c o r r e c t . C i r c u m f e r e n c e o f c i r c l e = 2 π R ∴ S t a t e m e n t (i i) i s i n c o r r e c t . A r e a o f c i r c l e = π R^{2} \frac{Area of circle}{Circumference of circle} = \frac{π R^{2}}{2 π R} = \frac{R}{2} ∴ S t a t e m e n t (i i i) i s c o r r e c t C i r c u m f e r e n c e o f c i r c l e = 2 π R L e t ’ s t a k e R = \frac{1}{2}, 2, 3 W h e n R = \frac{1}{2} A r e a = \frac{π}{4} P e r i m e t e r = π ∴ A r e a < P e r i m e t e r W h e n R = 2 A r e a = 4 π P e r i m e t e r = 4 π ∴ A r e a = P e r i m e t e r W h e n R = 3 A r e a = 9 π P e r i m e t e r = 6 π ∴ A r e a > P e r i m e t e r S o, r e l a t i o n b e t w e e n a r e a a n d p e r i m e t e r o f c i r c l e d e p e n d s u p o n i t s r a d i u s . S t a t e m e n t (i v) i s i n c o r r e c t .$

Topic Question Set

Q 1 :

The area of a quadrant of a circle, whose circumference is 22 cm, is

Q 2 :

The number of revolutions made by a circular wheel of radius 0.25m in rolling a distance of 11km is

Q 3 :

If the length of an arc of a circle subtending an angle $60 °$ at its centre is 22 cm, then the radius of the circle is :

Q 4 :

The diagonals of a rhombus ABCD intersect at O. Taking ‘O’ as the centre, an arc of radius 6 cm is drawn intersecting OA and OD at E and F respectively. The area of the sector OEF is :

Q 5 :

If the sum of the areas of two circles with radii $R_{1} a n d R_{2}$ is equal to the area of a circle of radius R , then:

Q 6 :

The area of the circle that can be inscribed in a square of side 6 cm is:

Q 7 :

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is:

Q 8 :

If the area of a circle is $64 π c m^{2}$ then its circumference is:

Q 9 :

If the areas of two circles are in the ratio 4:9, then the ratio of their perimeters of their semi-circles is:

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Topic Question Set

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Q 8 : If the area of a circle is 64π cm2 then its circumference is: .question-row { display: flex; align-items: flex-start; gap: 8px; } .q-no { font-size: 17px; white-space: nowrap; margin-left: -15px; } .q-text { font-size: 18px; flex: 1; } .q-no, .q-text p { line-height: 30px; }

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Q 1 :

The area of a quadrant of a circle, whose circumference is 22 cm, is

Q 6 :

The area of the circle that can be inscribed in a square of side 6 cm is:

Q 8 :

If the area of a circle is $64 π c m^{2}$ then its circumference is: