Answer it quickly . Two wires circles of diameter 28cm and 35cm are cut and then joined to form a big circle of radius k cm. Find the value of k .
Answers
Step by step explanation:
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
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Answer:First; we must find the perimeter of the two circles
Since the diameter is given in the equation,
Perimeter of a circle = 2πr, 2r=diameter so instead of multiplying it by two we can do, π x diameter
circle 1= 22/7 x 28 (it will get simplified as 22 x 4)
which is 88cm
circle 2= 22/7 x 35 (it will get simplified as 22 x 5)
which is 110cm
since it is mentioned in the question that the two circles are cut and then joined we must add the radii. (This is to find the perimeter of the big circle)
88+110=198cm.............(1)
Second; we must find the value of k, i.e. the radius of the big circle.
From (1) we know that the perimeter is 198cm.
substitute the values in the equation 'Perimeter of a circle = 2πr'
so, 198= 2 x 22/7 x r
198/2 = 22/7 x r
99÷22/7 = r....(22/7 will be reciprocated)
99 x 7/22 = r....(it will be simplified as 9x7/2)
=63/2
⇒31.5cm.
∴The radius of the big circle, i.e, k is 31.5cm.