PERIMETER OF SECTOR WORKSHEET
Problem 1 :
Find the perimeter of the sector PQR shown below.
Problem 2 :
Find the perimeter of the sector AOB shown below.
Problem 3 :
Find the perimeter of the sector BAP shown below.
Problem 4 :
Find the perimeter of the sector PQR shown below.
Problem 5 :
Find the perimeter of sector whose area is 324 square cm and the radius is 27 cm.
Problem 6 :
Find the length of arc, if the perimeter of sector is 45 cm and radius is 10 cm.
Problem 7 :
Find the radius of sector whose perimeter of the sector is 30 and length of the arc is 16 cm.
Problem 8 :
Find the diameter of the circle which has a sector whose perimeter is 84 cm and length of arc of the sector is 56 cm.
Solutions
Problem 1 :
Find the perimeter of the sector PQR shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 60°, r = 42 and ∏ = 22/7.
l = 60°/360° ⋅ 2 ⋅ 22/7 ⋅ 42
l = 1/6 ⋅ 2 ⋅ 22 ⋅ 6
l = 1 ⋅ 2 ⋅ 22
l = 44 cm
Perimeter of sector is
= l + 2r
Substitute l = 44 and r = 42.
= 44 + 2(42)
= 44 + 84
= 128 cm
So, length of the arc is 128 cm.
Problem 2 :
Find the perimeter of the sector AOB shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 120°, r = 21 and ∏ = 22/7.
l = 120°/360° ⋅ 2 ⋅ 22/7 ⋅ 21
l = 1/3 ⋅ 2 ⋅ 22 ⋅ 3
l = 1 ⋅ 2 ⋅ 22
l = 44 cm
Perimeter of sector is
= l + 2r
Substitute l = 44 and r = 21.
= 44 + 2(21)
= 44 + 42
= 86 cm
So, length of the arc is 86 cm.
Problem 3 :
Find the perimeter of the sector BAP shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 72°, r = 35 and ∏ = 22/7.
l = 72°/360° ⋅ 2 ⋅ 22/7 ⋅ 35
l = 1/5 ⋅ 2 ⋅ 22 ⋅ 5
l = 1 ⋅ 2 ⋅ 22
l = 44 cm
Perimeter of sector is
= l + 2r
Substitute l = 44 and r = 35.
= 44 + 2(35)
= 44 + 70
= 114 cm
So, length of the arc is 114 cm.
Problem 4 :
Find the perimeter of the sector PQR shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 36°, r = 10.5 and ∏ = 22/7.
l = 36°/360° ⋅ 2 ⋅ 22/7 ⋅ 10.5
l = 1/10 ⋅ 2 ⋅ 22 ⋅ 1.5
l = 66/10
l = 6.6 cm
Perimeter of sector is
= l + 2r
Substitute l = 6.6 and r = 10.5.
= 6.6 + 2(10.5)
= 6.6 + 21
= 27.6 cm
So, length of the arc is 27.6 cm.
Problem 5 :
Find the perimeter of sector whose area is 324 square cm and the radius is 27 cm.
Solution :
Area of sector = 324 cm2
rl / 2 = 324
Multiply each side by 2.
rl = 648
Substitute 27 for r.
27l = 648
Divide each side by 27.
l = 24 cm
Perimeter of sector is
= l + 2r
= 24 + 2(27)
= 24 + 54
= 78 cm
Problem 6 :
Find the length of arc, if the perimeter of sector is 45 cm and radius is 10 cm.
Solution :
Perimeter of sector = 45 cm
l + 2r = 45
Substitute 10 for r.
l + 2 (10) = 45
l + 20 = 45
l = 45 - 10
l = 35 cm
Problem 7 :
Find the radius of sector whose perimeter of the sector is 30 cm and length of the arc is 16 cm.
Solution :
Perimeter of sector = 30 cm
l + 2r = 30
Substitute 16 for l.
16 + 2r = 30
Subtract 16 from each side.
2r = 14
Divide each side by 2.
r = 7 cm
Problem 8 :
Find the diameter of the circle which has a sector whose perimeter is 84 cm and length of arc of the sector is 56 cm.
Solution :
Perimeter of sector = 84 cm
l + 2r = 84
Substitute 56 for l.
56 + 2r = 84
Subtract 56 from each side.
2r = 28
Diameter = 2 x Radius
Diameter = 2r
Diameter = 28 cm.
Apart from the stuff given in this section, 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
We always appreciate your feedback.
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
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
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
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
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
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 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
Recent Articles
-
Composition of Three Functions
Dec 02, 21 11:17 PM
Composition of Three Functions
-
Problems on Special Right Triangles
Dec 02, 21 10:19 PM
Problems on Special Right Triangles
-
Practice Problems Using Special Right Triangles
Dec 02, 21 10:13 PM
Practice Problems Using Special Right Triangles
