CIRCLES WORD PROBLEMS

Circles word problems :

Here we are going to see some practical problems based on the concept circles.

Area of circle  =  πr²

Circumference of circle  =  2πr

Example 1 :

The diameter of a cart wheel is 2.1 m. Find the distance travelled when it completes 100 revolutions.

Solution :

In order to find distance covered in one revolution, we have to find the circumference of the circle.

radius of wheel  =  2.1 / 2  =  1.05 m

Distance travelled when it completes 100 revolutions  =  1000 x circumference of the wheel

=  100 x 2 x (22/7) x (1.05)

=  100 x 2 x 22 x 0.15

=  660 m²

Example 2 :

The diameter of a circular park is 98 m. Find the cost of fencing it at \$4 per metre.

Solution :

Diameter of the circular park  =  98 m

radius  =  98/2  =  49 m

Cost of fencing  =  \$ 4 per meter

length covered by fencing  =  circumference of the circular park

Circumference of park  =  2πr

=  2 (22/7) x 49

=  2 x 22 x 7

=  308 m

Required cost for fencing  =  308 x 4  =  \$1232

Example 3 :

A wheel makes 20 revolutions to cover a distance of 66 m. Find the diameter of the wheel.

Solution :

Given :

A wheel makes 20 revolutions to cover a distance of 66 m

20 x one revolution  =  66 m

20 x 2πr  =  66

20 x 2 x (22/7) x  r  =  66

r  =  66 x (7/22) x (1/20) x (1/2)

r  =  21/40

r  =  0.525

Diameter  =  2r  =  2(0.525)  =  1.05 m

Example 4 :

The radius of a cycle wheel is 35 cm. How many revolutions does it make to cover a distance of 81.40 m?

Solution :

Radius of cycle wheel  =  35 cm  =  0.35 m

n x Revolution of cycle wheel  =  81.40

n x 2πr  =  81.40

n x 2 x (22/7) x 0.35  =  81.40

n  =  81.40/(2 x 22 x 0.05)

n  =  81.40/2.2

n  =  37

Hence the cycle wheel has to revolve 374 times to cover the distance.

Example 5 :

The radius of a circular park is 63 m. Find the cost of fencing it at \$12 per metre.

Solution :

Radius of the circular park  =  63 m

Length of fencing  =  Circumference of circular park

=   2πr   =  2 x (22/7) x 63

=  2 x 22 x 9

=  396 m

Cost of fencing  = \$ 12 per meter

Total cost for fencing  =  396 x 12

=  \$4752

Example 6 :

A goat is tethered by a rope 3.5 m long. Find the maximum area that the goat can graze.

Solution :

Radius of the circle = Length of the rope

radius r = 3.5 m = 7/2 m

Maximum area grazed by the goat = πr²sq. units.

= (22/7) x (7/2) x (7/2)

=  77/2  =  38.5 sq. m

Maximum area grazed by the goat is 38.5 sq. m.

Example 7 :

The circumference of a circular park is 176 m. Find the area of the park.

Solution :

Circumference = 176 m (given)

2πr = 176

2 x (22/7) x r  =  176

44 r /7  =  176

r  =  (176 x 7)/44

r  =  28 m

Area of the park = πr²

=  (22/7) x 28 x 28

= 22 x 4 x 28

= 2464 sq. m.

Example 8 :

A silver wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent in the form of a circle. Find the area of the circle.

Solution :

Let a be the side of the square

Area of the square = 121 sq. cm. (given)

a² = 121, a² = 11 cm (11 x 11 = 121)

Perimeter of the square = 4a units

= 4 x 11 cm

= 44 cm

Length of the wire = Perimeter of the square

= 44 cm

The wire is bent in the form of a circle

The circumference of the circle = Length of the wire

Circumference of a circle = 44 cm

2πr = 44

2 x (22/7) x r  =  44

r = 44 x (7/22) x (1/2)

r  =  7 cm

Area of the circle = πr²

= (22/7) x 7 x 7

Area of the circle = 154 cm²

After having gone through the stuff given above, we hope that the students would have understood "Circles word problems".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

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Complementary and supplementary angles word problems

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Trigonometry word problems

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Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

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Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

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Profit and loss shortcuts

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Time, speed and distance shortcuts

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Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

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Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6
The text passage contains multiple word problems related to circles, each with a question and a corresponding solution.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
CIRCLES WORD PROBLEMS

Circles word problems :

Here we are going to see some practical problems based on the concept circles.

Area of circle  =  πr²

Circumference of circle  =  2πr

Example 1 :

The diameter of a cart wheel is 2.1 m. Find the distance travelled when it completes 100 revolutions.

Solution :

In order to find distance covered in one revolution, we have to find the circumference of the circle.

radius of wheel  =  2.1 / 2  =  1.05 m

Distance travelled when it completes 100 revolutions  =  1000 x circumference of the wheel

=  100 x 2 x (22/7) x (1.05)

=  100 x 2 x 22 x 0.15

=  660 m²

Example 2 :

The diameter of a circular park is 98 m. Find the cost of fencing it at \$4 per metre.

Solution :

Diameter of the circular park  =  98 m

radius  =  98/2  =  49 m

Cost of fencing  =  \$ 4 per meter

length covered by fencing  =  circumference of the circular park

Circumference of park  =  2πr

=  2 (22/7) x 49

=  2 x 22 x 7

=  308 m

Required cost for fencing  =  308 x 4  =  \$1232

Example 3 :

A wheel makes 20 revolutions to cover a distance of 66 m. Find the diameter of the wheel.

Solution :

Given :

A wheel makes 20 revolutions to cover a distance of 66 m

20 x one revolution  =  66 m

20 x 2πr  =  66

20 x 2 x (22/7) x  r  =  66

r  =  66 x (7/22) x (1/20) x (1/2)

r  =  21/40

r  =  0.525

Diameter  =  2r  =  2(0.525)  =  1.05 m

Example 4 :

The radius of a cycle wheel is 35 cm. How many revolutions does it make to cover a distance of 81.40 m?

Solution :

Radius of cycle wheel  =  35 cm  =  0.35 m

n x Revolution of cycle wheel  =  81.40

n x 2πr  =  81.40

n x 2 x (22/7) x 0.35  =  81.40

n  =  81.40/(2 x 22 x 0.05)

n  =  81.40/2.2

n  =  37

Hence the cycle wheel has to revolve 374 times to cover the distance.

Example 5 :

The radius of a circular park is 63 m. Find the cost of fencing it at \$12 per metre.

Solution :

Radius of the circular park  =  63 m

Length of fencing  =  Circumference of circular park

=   2πr   =  2 x (22/7) x 63

=  2 x 22 x 9

=  396 m

Cost of fencing  = \$ 12 per meter

Total cost for fencing  =  396 x 12

=  \$4752

Example 6 :

A goat is tethered by a rope 3.5 m long. Find the maximum area that the goat can graze.

Solution :

Radius of the circle = Length of the rope

radius r = 3.5 m = 7/2 m

Maximum area grazed by the goat = πr²sq. units.

= (22/7) x (7/2) x (7/2)

=  77/2  =  38.5 sq. m

Maximum area grazed by the goat is 38.5 sq. m.

Example 7 :

The circumference of a circular park is 176 m. Find the area of the park.

Solution :

Circumference = 176 m (given)

2πr = 176

2 x (22/7) x r  =  176

44 r /7  =  176

r  =  (176 x 7)/44

r  =  28 m

Area of the park = πr²

=  (22/7) x 28 x 28

= 22 x 4 x 28

= 2464 sq. m.

Example 8 :

A silver wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent in the form of a circle. Find the area of the circle.

Solution :

Let a be the side of the square

Area of the square = 121 sq. cm. (given)

a² = 121, a² = 11 cm (11 x 11 = 121)

Perimeter of the square = 4a units

= 4 x 11 cm

= 44 cm

Length of the wire = Perimeter of the square

= 44 cm

The wire is bent in the form of a circle

The circumference of the circle = Length of the wire

Circumference of a circle = 44 cm

2πr = 44

2 x (22/7) x r  =  44

r = 44 x (7/22) x (1/2)

r  =  7 cm

Area of the circle = πr²

= (22/7) x 7 x 7

Area of the circle = 154 cm²

After having gone through the stuff given above, we hope that the students would have understood "Circles word problems".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6
user
The text passage contains multiple word problems related to circles, each with a question and a corresponding solution.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS