Question

find the diameter of a circle whose circumference is 5.5km​

Answer 1

★ The diameter of the circle is 1.75 km.

Step-by-step explanation

Question analysis -

‎ ‎ ‎ ‎ ‎ ‎ ‎It is given that the circumference (perimeter) of a circle is 5.5 km and the measure of its diameter has been asked to find.

Solution -

We know that the formula for perimeter of circle

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ $\sf \pmb{P=2\pi r \: units}$

Here, the known values are:

$\twoheadrightarrow$ $\pi$ = 3.14

$\twoheadrightarrow$ P = 5.5 km

The unknown value is the measure of radius. Let's know the relation between the radius and the diameter in a circle!

• Diameter (D) is the longest chord in a circle, which equals double the length of the radius (r).
• So, here forms the equations:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎D = 2r ... eqn - 1

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎r = 1/2 × D ... eqn - 2

According to the analysis, the measure of diameter is required. Now, on substituting the known values in the formula of perimeter of circle gives the measure of radius.

$\dashrightarrow{ \sf{P = 2\pi r}} \\ \\ \dashrightarrow{ \sf{5.5 = 2 \times 3.14 \times r}} \\ \\ \dashrightarrow{ \sf{5.5 = 6.28 \times r}} \\ \\ \dashrightarrow{ \sf{\dfrac{5.5}{6.28} = r }} \\ \\ \dashrightarrow{\sf \pmb{0.875 \: km = r}}$

Finally, on substituting the value of radius in first equation gives the required answer.

$\twoheadrightarrow$ D = 2r

$\twoheadrightarrow$ D = 2(0.875)

$\twoheadrightarrow$ D = 1.75 km

Therefore, the length of diameter of the circle is 1.75 km.

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Answer 2

Given : The Circumference of a circle is 5.5 km .

Exigency to Find : Diameter of Circle.

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DIAGRAM :

$\setlength{\unitlength}{1mm}\begin{picture}(50,55)\linethickness{0.4mm}\qbezier(45,30)(45,30)(5,30)\qbezier(25.000,10.000)(33.284,10.000)(39.142,15.858)\qbezier(39.142,15.858)(45.000,21.716)(45.000,30.000)\qbezier(45.000,30.000)(45.000,38.284)(39.142,44.142)\qbezier(39.142,44.142)(33.284,50.000)(25.000,50.000)\qbezier(25.000,50.000)(16.716,50.000)(10.858,44.142)\qbezier(10.858,44.142)( 5.000,38.284)( 5.000,30.000)\qbezier( 5.000,30.000)( 5.000,21.716)(10.858,15.858)\qbezier(10.858,15.858)(16.716,10.000)(25.000,10.000)\multiput(5,30)(20,0){3}{\circle*{1}}\end{picture}$

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⠀⠀⠀⠀⠀ Finding the Radius of Circle to find Diameter :

❍ Let's Consider the Radius of Circle be r km .

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{Circumference _{(Circle)} \:: 2\pi r }\bigg\rgroup$

⠀⠀⠀⠀⠀Here , r is the Radius of Circle & $\pi \:= \:\dfrac{22}{7} \:$ and we know that Circumference of Circle is 5.5 km .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf 5.5 = 2 \times \dfrac{22}{7} \times r$

$\qquad:\implies \sf 5.5 = 2 \times 3.14 \times r$

$\qquad:\implies \sf 5.5 = 6.28 \times r$

$\qquad:\implies \sf \dfrac{5.5}{6.28} = r$

$\qquad:\implies \sf \cancel {\dfrac{5.5}{6.28}} = r$

$\qquad :\implies \frak{\underline{\purple{\:r = 0.875 \:km\: \:}} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Radius \:of\:Circle \:is\:\bf{0.875\:km\:.}}}}$

⠀⠀⠀⠀⠀Finding Diameter of Circle :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{Diameter _{(Circle)} \:: 2 \times r }\bigg\rgroup$

⠀⠀⠀⠀⠀Here , r is the Radius of Circle .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf Diameter \:=\: 2 \times 0.875$

$\qquad:\implies \sf Diameter \:=\: 1.75$

$\qquad :\implies \frak{\underline{\purple{\:Diameter \:= 1.75\:km\: }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Hence,\:Diameter \:of\:Circle \:is\:\bf{1.75\:km\:.}}}}$

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Note : For Diagram Kindly view this Answer in website [ brainly.in ] .

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