Two wire circle of diameter 28cm and 35 cm are cut and then join to form a big circle of radius k centimetre find the value of k
Answers
Find the circumference of the circle with diameter 28 cm:
Circumference = πD
= π(28)
= 28π cm
Find the circumference of the circle with diameter 35 cm:
Circumference = πD
= π(35)
= 35π cm
Find the Circumference of the big circle:
Total length = 28π + 35π
= 63π cm
Find the Diameter:
Diameter = Circumference ÷ π
= 63π ÷ π
= 63 cm
Find the radius:
Radius = Diameter ÷ 2
= 63 ÷ 2
= 31.5 cm
Answer: The radius, k , is 31.5 cm
Two circles have the diameters 28 cm and 35 cm
If we cut them and join them to form a big circle:
then the diameters of the small circles when added will equal the big circle's diameter
Circumference of a circle is πd
where d is the diameter of the circle.
So:
diameter of the first circle is 28 cm
==> C=πd
==>C=28πcm
Its better to keep it in pi so that later you may change it:
Next circle has a diameter 35 cm
==> C=πd
==>C=35πcm
Now if both the circumferences are added then it will give the circumference of the big circle.
So:
C=35πcm+28πcm
==> C= π(35 cm+28 cm)
==>C=63πcm
We know that:
C=πd
Hence:
πd=63πcm
==> Cancel π both sides
==> d=63 cm
We know that radius is twice the diameter.
Hence:
==> 2r=63 cm
==>r=63/2 cm
==>r=31.5 cm
The radius is of k centimeters
Hence k is 31.5
The value of k is 31.5 cm
Thanks for the question
Have a nice day
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