## AREA OF SECTOR WORKSHEET

Problem 1 :

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Problem 2 :

Find the area of the sector that is outlined with the bold line. (Take π = 3.14 and round your answer to one decimal place, if necessary) Problem 3 :

Find the area of the sector that is outlined with the bold line. (Take π = 3.14 and round your answer to one decimal place, if necessary) Problem 4 :

In the diagram given below, LMN is a central angle and m∠LMN  =  78° and radius is 4 cm. find the area of sector LMN. (Take π = 3.14 and round your answer to one decimal place, if necessary) Problem 5 :

In circle C, if XCZ is a central angle and XYZ is an inscribed angle and m∠XYZ  =  58° and radius is 10 inches. Find the area of sector XCZ. (Take π = 3.14 and round your answer to one decimal place, if necessary) Problem 6 :

If QRS is a central angle and m∠QRS = 46°, m∠SRT = 80°, and diameter is 4 inches, then find the area of the shaded sector. (Take π = 3.14 and round your answer to one decimal place, if necessary) Problem 7 :

If the sector area of a sector intersecting Arc AB is 37 square cm and the radius is 11, then find the measure of Arc AB. (Take π = 3.14 and round your answer to the nearest whole number)

Problem 8 :

Find the area of the sector and the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm. (Take π = 3.14 and round your answer to the nearest whole number)

Problem 9 :

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

Problem 10 :

If the sector area of a sector intersecting Arc AB is 43 square cm and the measure of Arc AB is 43°, then find the radius. (Take π = 3.14 and round your answer to one decimal place, if necessary) Problem 1 :

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution :

The formula to find area of the sector is

=  (θ / 360°⋅ πr2

Plug r  =  42, θ  =  60° and π    3.14

(60° / 360°⋅ 3.14  422

923. 2

So, the area of the sector is about 923.2 cm2.

Problem 2 :

Find the area of the sector that is outlined with the bold line. (Take π = 3.14 and round your answer to one decimal place, if necessary) Solution :

The formula to find area of the sector is

=  (θ / 360°⋅ πr2

Plug r  =  6, θ  =  45° and π    3.14

(45° / 360°⋅ 3.14  62

14.1

So, the area of the given sector is about 14.1 yd2.

Problem 3 :

Find the area of the sector that is outlined with the bold line. (Take π = 3.14 and round your answer to one decimal place, if necessary) Solution :

The formula to find area of the sector is

=  (θ / 360°⋅ πr2

Plug r  =  11, θ  =  300° and π    3.14

(300° / 360°⋅ 3.14  112

316.7

So, the area of the given sector is about 316.7 cm2.

Problem 4 :

In the diagram given below, LMN is a central angle and m∠LMN  =  78° and radius is 4 cm. find the area of sector LMN. (Take π = 3.14 and round your answer to one decimal place, if necessary) Solution :

The formula to find area of the sector is

=  (θ / 360°⋅ πr2

Plug r  =  4, θ  =  78° and Π    3.14

(78° / 360°⋅ 3.14  42

10.9

So, the area of sector LMN is about 10.9 cm2.

Problem 5 :

In circle C, if XCZ is a central angle and XYZ is an inscribed angle and m∠XYZ  =  58° and radius is 10 inches. Find the area of sector XCZ. (Take π = 3.14 and round your answer to one decimal place, if necessary) Solution :

By Inscribed Angle Theorem, we have

1/2 ⋅ m∠XCZ  =  m∠XYZ

Multiply both sides by 2.

m∠XCZ  =  2 ⋅ m∠XYZ

Given : m∠XYZ  =  58°.

Then, we have

m∠XCZ  =  2 ⋅ 58°

m∠XCZ  =  116°

So, the central angle θ is 116°.

The formula to find area of the sector is

=  (θ / 360°⋅ πr2

Plug r  =  10, θ  =  116° and Π    3.14

(116° / 360°⋅ 3.14  102

101.2

So, the area of sector XCZ is about 101.2 in2.

Problem 6 :

If QRS is a central angle and m∠QRS = 46°, m∠SRT = 80°, and diameter is 4 inches, then find the area of the shaded sector. (Take π = 3.14 and round your answer to one decimal place, if necessary) Solution :

Given : m∠QRS  =  46° and m∠SRT  =  80°.

Then, we have

m∠QRS + m∠SRT  =  46° + 80°

m∠QRS + m∠SRT  =  126°

Measure of central angle of the shaded region :

m∠QRT  =  360° - 126°

m∠QRT  =  234°

The formula to find area of the sector is

=  (θ / 360°⋅ πr2

Plug r  =  2, θ  =  234° and Π    3.14

(234° / 360°⋅ 3.14  22

8.2

Problem 7 :

If the sector area of a sector intersecting Arc AB is 37 square cm and the radius is 11, then find the measure of Arc AB. (Take π = 3.14 and round your answer to the nearest whole number)

Solution :

Given : A sector is intersecting Arc AB.

Because the given sector is intersecting Arc AB, the measure of Arc AB is nothing but the central angle of the given sector.

Given : Area of the sector is 37 square cm.

Then, we have

(θ / 360°⋅ πr2  =  37

Plug r  =  11 and π    3.14

(θ / 360°⋅ 3.14  112  =  37

(θ / 360°⋅ 3.14  112  =  37

(θ / 360°⋅ 379.94  =  37

Divide both sides by 379.94

(θ / 360°)  =  37 / 379.94

(θ / 360°)  =  0.09738

Multiply both sides by 360°.

θ  =  0.09738 ⋅ 360°

θ  ≈  35

So, the measure of Arc AB is about 35°.

Problem 8 :

Find the area of the sector and the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm. (Take π = 3.14 and round your answer to the nearest whole number)

Solution :

The formula to find area of the sector is

=  (l ⋅ r) / 2

Plug l  =  66 and r  =  21.

=  (66 ⋅ 21) / 2

=  693

So, the area of the sector is 693 cm².

Central angle formed by the sector :

Area of the sector  =  693

(θ / 360°⋅ πr2  =  693

(θ / 360°) ⋅ 3.14  212  =  693

(θ / 360°) ⋅ 1384.74  =  693

Multiply both sides by 1384.74 / 360°.

θ  ⋅ (360° / 1384.74)

θ  ≈  180°

So, the area of the sector is 693 square cm and the measure of central angle is 180°.

Problem 9 :

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

Solution :

Formula to find perimeter of a sector :

Perimeter  =  length of the arc +  2 ⋅ radius

or

P  =  l + 2r

Given : Perimeter of the sector is 147 cm and the radius is 35 cm.

Then, we have

l + 2 ⋅ 35  =  147

l + 70  =  147

Subtract 70 from both sides.

l  =  77

The formula to find area of the sector is

=  (l ⋅ r) / 2

Plug l  =  77 and r  =  35

=  (77 ⋅ 35) / 2

=  1347.5

So, the area of the sector is 1347.5 cm2.

Problem 10 :

If the sector area of a sector intersecting Arc AB is 43 square cm and the measure of Arc AB is 43°, then find the radius. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution :

Given : The measure of Arc AB is 43°

Because the given sector is intersecting Arc AB, the measure of Arc AB is nothing but the central angle of the given sector.

Then, the measure of central angle of the sector is 43°.

Given : Area of the sector is 37 square cm.

Then, we have

(θ / 360°⋅ πr2  =  43

Plug θ  =  43° and π    3.14

(43° / 360°⋅ 3.14  r2  =  43

Divide both sides by 3.14

(43° / 360°r2  =  43 / 3.14

0.1194 ⋅ r2  =  13.6943

r2  =  13.6943 / 0.1194

r2  =  11.7834 / 0.1194

r2  =  114.6926

r  ≈  10.7 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

You can also visit the 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

1. Click on the HTML link code below.

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 