Class 10 maths Areas Related to Circles Hots Questions

Q 1 :

Raju installed a fence around a circular field, with the total cost amounting to Rs 6,000 at a rate of Rs 30 per m. He now plans to plough the field.

Based on the above information answer the following questions:

(i) What is the perimeter of the field?

200 m
400 m
600 m
300 m

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(1)

Let r m be the radius of the circular field.

$∴ L e n g t h o f f e n c e = P e r i m e t e r o f c i r c l e = 2 π r T o t a l c o s t o f f e n c i n g = 2 π r \times 30 6000 = 60 π r \Rightarrow 100 = π r \Rightarrow r = \frac{100}{π} (i) P e r i m e t e r o f t h e f i e l d 2 π r = 2 π \times \frac{100}{π} = 200 m$

Q 2 :

Raju installed a fence around a circular field, with the total cost amounting to Rs 6,000 at a rate of Rs 30 per m. He now plans to plough the field.

Based on the above information answer the following questions:

(ii) What is the radius of the field?

$1 \frac{8}{11} m$
$1 \frac{9}{11} m$
$1 \frac{9}{10} m$
$2 \frac{9}{11} m$

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(2)

Radius of the field

$r = \frac{100}{π} = \frac{700}{22} = \frac{350}{11} = 31 \frac{9}{11} m$

Q 3 :

Raju installed a fence around a circular field, with the total cost amounting to Rs 6,000 at a rate of Rs 30 per m. He now plans to plough the field.

Based on the above information answer the following questions:

(iii) (a) What is the area of the field?

$2181.81 m^{2}$
$3181.82 m^{2}$
$3180.82 m^{2}$
$3181.81 m^{2}$

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(4)

Area of the field

$π r^{2} = π \times {(\frac{100}{π})}^{2} = π \times \frac{100 \times 100}{π^{2}} = \frac{10000}{π} = \frac{10000}{\frac{22}{7}} = \frac{70000}{22} \approx 3181.81 m^{2}$

Q 4 :

A brooch is a small piece of jewelry that features a pin on the back, allowing it to be fastened to a dress, blouse, or coat. Below are designs for some brooches.

Design A: Brooch A is crafted from silver wire in the shape of a circle with a diameter of 28 mm. The wire is also used to create 4 diameters, dividing the circle into 8 equal parts.

Design B: Brooch B is made with two colors, gold and silver. The outer portion is made of gold. The circumference of the silver section is 44 mm, and the gold section is uniformly 3 mm wide.

Based on the above information answer the following questions:

(i) In design A, what is the total length of the wire required?

200 m
400 m
600 m
500 m

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(1)

In design A, diameter of the circle is 28 mm.

$∴ Circumference of the circle = π \times 28 mm = \frac{22}{7} \times 28 mm = 88 mm$

$Length of the wire used in 4 diameters$

$= 4 \times 28 mm = 112 mm$

$∴ Total length of the required wire = (112 + 88) mm = 200 mm$

Q 5 :

Raju installed a fence around a circular field, with the total cost amounting to Rs 6,000 at a rate of Rs 30 per m. He now plans to plough the field.

Based on the above information answer the following questions:

(iii) (b) Find the cost of ploughing the field at the rate of $R s 0.50 p e r m ² .$

$1591.90$
$- 1590.90$
$1490.90$
$1590.90$

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(4)

Total cost of ploughing the field

$3181.81 \times 0.50 = R s 1590.90$

Q 6 :

A brooch is a small piece of jewelry that features a pin on the back, allowing it to be fastened to a dress, blouse, or coat. Below are designs for some brooches.

Design A: Brooch A is crafted from silver wire in the shape of a circle with a diameter of 28 mm. The wire is also used to create 4 diameters, dividing the circle into 8 equal parts.

Design B: Brooch B is made with two colors, gold and silver. The outer portion is made of gold. The circumference of the silver section is 44 mm, and the gold section is uniformly 3 mm wide.

Based on the above information answer the following questions:

(ii) In design A, what is the area of each part of the brooch?

$77 m m^{2}$
$55 m m^{2}$
$70 m m^{2}$
$72 m m^{2}$

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(1)

Area of each part of brooch

$= \frac{1}{8} (Area of the circle) = (\frac{1}{8} \times \frac{22}{7} \times 14^{2}) {mm}^{2} = 77 m m^{2}$

Q 7 :

A brooch is a small piece of jewelry that features a pin on the back, allowing it to be fastened to a dress, blouse, or coat. Below are designs for some brooches.

Design A: Brooch A is crafted from silver wire in the shape of a circle with a diameter of 28 mm. The wire is also used to create 4 diameters, dividing the circle into 8 equal parts.

Design B: Brooch B is made with two colors, gold and silver. The outer portion is made of gold. The circumference of the silver section is 44 mm, and the gold section is uniformly 3 mm wide.

Based on the above information answer the following questions:

(iii) (a) In design B, find the circumference of the outer part (golden).

7 mm
6 mm
5 mm
4 mm

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(1)

Let r mm be the radius of the silver part. Then,

$2 \times \frac{22}{7} \times r = 44 \Rightarrow r = 7 mm .$

Q 8 :

A brooch is a small piece of jewelry that features a pin on the back, allowing it to be fastened to a dress, blouse, or coat. Below are designs for some brooches.

Design A: Brooch A is crafted from silver wire in the shape of a circle with a diameter of 28 mm. The wire is also used to create 4 diameters, dividing the circle into 8 equal parts.

Design B: Brooch B is made with two colors, gold and silver. The outer portion is made of gold. The circumference of the silver section is 44 mm, and the gold section is uniformly 3 mm wide.

Based on the above information answer the following questions:

(iii) (b) A boy is playing with brooch B. He makes revolutions with it along its edge. How many complete revolutions must it take it cover $80 π m m ?$

n = 6
n = 4
n = 3
n = 2

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(2)

Outer circumference of Brooch B:

$= 2 π \times 10 mm = 20 π mm Suppose to cover 80 π mm brooch B takes ncomplete revolutions . Then, 20 π \times n = 80 π \Rightarrow n = 4$

Q 9 :

A stable owner has four horses. He usually ties these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.

Based on the above information answer the following questions:

(i) Find the area of the square shaped grass field.

$200 m^{2}$
$400 m^{2}$
$100 m^{2}$
$250 m^{2}$

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(2)

Area of the square shaped grass field $= 20 m \times 20 m = 400 m^{2}$

Q 10 :

A stable owner has four horses. He usually ties these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.

Based on the above information answer the following questions:

(ii) (a) Find the area of the total field in which these horses can graze.

$150 m^{2}$
$152 m^{2}$
$145 m^{2}$
$154 m^{2}$

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(4)

Area of the total field in which these horses can graze

$= 4 \times \frac{90 °}{360 °} \times π r^{2} = π r^{2} = \frac{22}{7} \times (7)^{2} = 154 m^{2}$

Topic Question Set

Q 1 :

Raju installed a fence around a circular field, with the total cost amounting to Rs 6,000 at a rate of Rs 30 per m. He now plans to plough the field.

Based on the above information answer the following questions:

(i) What is the perimeter of the field?

Q 2 :

Raju installed a fence around a circular field, with the total cost amounting to Rs 6,000 at a rate of Rs 30 per m. He now plans to plough the field.

Based on the above information answer the following questions:

(ii) What is the radius of the field?

Q 3 :

Raju installed a fence around a circular field, with the total cost amounting to Rs 6,000 at a rate of Rs 30 per m. He now plans to plough the field.

Based on the above information answer the following questions:

(iii) (a) What is the area of the field?

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