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Find the diameter of a circle whose circumference is equal to the sum of the circumference of the two circles of diameter $36$ m and $20$ m.

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Last updated date: 20th Jun 2024
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Answer
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Hint: In this example, we will use the formula of the circumference of a circle is $\pi d$ where $d$ is the diameter of the circle. We will use the given condition that the circumference of one circle is equal to the sum of circumference of two circles of diameter $36$ m and $20$ m.

Complete step by step answer:
Let us assume that $C$ is the circle whose diameter is $d$. Therefore, the circumference of circle $C$ is $\pi d$. Let us assume that ${C_1},{C_2}$ are two circles with diameter ${d_1} = 36$ m and ${d_2} = 20$ m respectively. Therefore, the circumference of circle ${C_1}$ is $\pi {d_1} = 36\pi $ and circumference of circle ${C_2}$ is $\pi {d_2} = 20\pi $. Now we will use the given condition that circumference of circle $C$ is equal to the sum of circumference of circles ${C_1}$ and ${C_2}$ of diameter $36$ m and $20$ m. Therefore, we can write$\pi d = \pi {d_1} + \pi {d_2}$
Cancelling π from both sides, we get
$d = {d_1} + {d_2}$
$ \Rightarrow d = 36 + 20$
$ \Rightarrow d = 56$ m
Hence, the diameter of the required circle is $56$ m.

Note:
Radius is the distance between the center of the circle and any point lying on the circle. The diameter is the distance across the circle through the center. Radius is half of the diameter. That is, twice the radius of a circle is the diameter of a circle. If we know the diameter of the circle then we can find the radius and it is given by $r = \dfrac{d}{2}$. Also, we can write the circumference of the circle is $2\pi r$. The circumference of the circle is also called the perimeter of the circle. It is the measurement of the boundary of the circle. The ratio of circumference to the diameter of the circle is $\pi $.