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Answer :
Final answer:
To solve for missing elements in circle geometry problems, use the formulas Circumference (C) = 2πr and Area (A) = πr², with π approximated as 3.14. Here, r represents the circle's radius. Apply these formulas to fill in the missing values for radius, diameter, circumference, and area.
Explanation:
Solving for Missing Elements in Circle Geometry
To solve the missing elements for each problem, we apply the formulas for the circumference and area of a circle using 3.14 for π (pi). The formulas to remember are: Circumference (C) = 2πr and Area (A) = πr², where 'r' represents the radius of the circle, and the diameter (D) is simply twice the radius (D = 2r).
Let's solve one example to illustrate:
The student can follow this example to solve for the missing elements in other given problems, using the correct values for the radius as provided or derived from the given diameters.
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Rewritten by : Barada
we know that
diameter=radius*2
radius=diameter/2
area of circle=pi*r²
length of circumference=2*pi*r
so
Part 1) 4 inches circumference
4=2*pi*r--------> r=4/(2*pi)-----> r=2/pi-----> r=0.64 in
diameter=2*0.64-----> 1.28 in
area=pi*0.64²------> 1.29 in²
the answers Part 1) are
a) radius=0.64 in
b) diameter=1.28 in
c) area=1.29 in²
Part 2) 10 ft circumference
10=2*pi*r-----> r=10/(2*pi)----> r=5/pi-----> 1.59 ft
diameter=2*1.59------> 3.18 ft
area=pi*1.59²-----> 7.94 ft²
the answers Part 2) are
a) radius=1.59 ft
b) diameter=3.18 ft
c) area=7.94 ft²
Part 3) 18 yards diameter
radius=18/2-----> 9 yd
circumference=2*pi*9-----> 56.52 yd
area=pi*9²-----> 254.34 yd²
the answers part 3) are
radius=9 yd
circumference=56.52 yd
area=254.34 yd²
Part 4) 16 cm circumference
16=2*pi*r-----> r=16/(2*pi)----> r=8/pi-----> 2.55 cm
diameter=2*2.55------> 5.10 cm
area=pi*2.55²-----> 20.42 cm²
the answers Part 4) are
a) radius=2.55 cm
b) diameter=5.10 cm
c) area=20.42 cm²
Part 5) 19 mm diameter
radius=19/2-----> 9.5 mm
circumference=2*pi*9.5-----> 59.66 mm
area=pi*9.5²-----> 283.39 mm²
the answers part 5) are
radius=9.5 mm
circumference=59.66 mm
area=283.39 mm²
Part 6) 12 inches diameter
radius=12/2-----> 6 in
circumference=2*pi*6-----> 37.68 in
area=pi*6²-----> 113.04 in²
the answers part 6) are
radius=6 in
circumference=37.68 in
area=113.04 in²
Part 7) 28 ft circumference
28=2*pi*r-----> r=28/(2*pi)----> r=14/pi-----> 4.46 ft
diameter=2*4.46------> 8.92 ft
area=pi*4.46²-----> 62.46 ft²
the answers Part 7) are
a) radius=4.46 ft
b) diameter=8.92 ft
c) area=62.46 ft²
Part 8) 6 yards diameter
radius=6/2-----> 3 yd
circumference=2*pi*3-----> 18.84 yd
area=pi*3²-----> 28.26 yd²
the answers part 8) are
radius=3 yd
circumference=18.84 yd
area=28.26 yd²
Part 9) 18 cm circumference
18=2*pi*r-----> r=18/(2*pi)----> r=9/pi-----> 2.87 cm
diameter=2*2.87------> 5.74 cm
area=pi*2.87²-----> 25.86 cm²
the answers Part 9) are
a) radius=2.87 cm
b) diameter=5.74 cm
c) area=25.86 cm²
diameter=radius*2
radius=diameter/2
area of circle=pi*r²
length of circumference=2*pi*r
so
Part 1) 4 inches circumference
4=2*pi*r--------> r=4/(2*pi)-----> r=2/pi-----> r=0.64 in
diameter=2*0.64-----> 1.28 in
area=pi*0.64²------> 1.29 in²
the answers Part 1) are
a) radius=0.64 in
b) diameter=1.28 in
c) area=1.29 in²
Part 2) 10 ft circumference
10=2*pi*r-----> r=10/(2*pi)----> r=5/pi-----> 1.59 ft
diameter=2*1.59------> 3.18 ft
area=pi*1.59²-----> 7.94 ft²
the answers Part 2) are
a) radius=1.59 ft
b) diameter=3.18 ft
c) area=7.94 ft²
Part 3) 18 yards diameter
radius=18/2-----> 9 yd
circumference=2*pi*9-----> 56.52 yd
area=pi*9²-----> 254.34 yd²
the answers part 3) are
radius=9 yd
circumference=56.52 yd
area=254.34 yd²
Part 4) 16 cm circumference
16=2*pi*r-----> r=16/(2*pi)----> r=8/pi-----> 2.55 cm
diameter=2*2.55------> 5.10 cm
area=pi*2.55²-----> 20.42 cm²
the answers Part 4) are
a) radius=2.55 cm
b) diameter=5.10 cm
c) area=20.42 cm²
Part 5) 19 mm diameter
radius=19/2-----> 9.5 mm
circumference=2*pi*9.5-----> 59.66 mm
area=pi*9.5²-----> 283.39 mm²
the answers part 5) are
radius=9.5 mm
circumference=59.66 mm
area=283.39 mm²
Part 6) 12 inches diameter
radius=12/2-----> 6 in
circumference=2*pi*6-----> 37.68 in
area=pi*6²-----> 113.04 in²
the answers part 6) are
radius=6 in
circumference=37.68 in
area=113.04 in²
Part 7) 28 ft circumference
28=2*pi*r-----> r=28/(2*pi)----> r=14/pi-----> 4.46 ft
diameter=2*4.46------> 8.92 ft
area=pi*4.46²-----> 62.46 ft²
the answers Part 7) are
a) radius=4.46 ft
b) diameter=8.92 ft
c) area=62.46 ft²
Part 8) 6 yards diameter
radius=6/2-----> 3 yd
circumference=2*pi*3-----> 18.84 yd
area=pi*3²-----> 28.26 yd²
the answers part 8) are
radius=3 yd
circumference=18.84 yd
area=28.26 yd²
Part 9) 18 cm circumference
18=2*pi*r-----> r=18/(2*pi)----> r=9/pi-----> 2.87 cm
diameter=2*2.87------> 5.74 cm
area=pi*2.87²-----> 25.86 cm²
the answers Part 9) are
a) radius=2.87 cm
b) diameter=5.74 cm
c) area=25.86 cm²
