The sum of the circumferences and diameter of a circle is 116cm . Find its radius. pls solve this on any notebook About the author Adalynn
Question : The sum of the circumferences and diameter of a circle is 116cm . Find its radius. Formulas : ●Circumference of circle = 2πr ●Diameter of circle = 2r Solution : Circumference + diameter = 116 [tex] \tt \implies [/tex] 2πr + 2r = 116 [tex] \tt \implies [/tex] 2r(π+1) =116 [tex] \tt \implies [/tex] r([tex] \tt \frac{22}{7}[/tex] + 1 ) = [tex] \tt \frac{116}{2}[/tex] [tex] \tt \implies [/tex] r([tex]\tt \frac{22+7}{7}[/tex]) = 58 [tex] \tt \implies [/tex] r = 58 × [tex] \tt \frac{7}{29}[/tex] [tex] \tt \implies [/tex] r = 2 × 7 [tex] \tt \implies [/tex] r = 14 cm [tex] \tt \therefore [/tex] Radius of circle is 14 cm Reply
[tex]\sf\small\underline\red{Given:-}[/tex] [tex]\sf{\implies Sum\:_{(circumference+diameter)}=116}[/tex] [tex]\sf\small\underline\red{To\: Find:-}[/tex] [tex]\sf{\implies Radius\:of\:_{(circle)}=?}[/tex] [tex]\sf\small\underline\red{Solution:-}[/tex] By applying formula to calculate the radius of circle as we know that diameter of circle is 2r and circumference of circle is 2πr. [tex]\sf\small\underline\red{Formula\:used:-}[/tex] [tex]\sf\longrightarrow{Circumference\:_{(circle)}=2\pi\:r}[/tex] [tex]\sf\longrightarrow{Diameter\:_{(circle)}=2r}[/tex] [tex]\bf{\implies Circle\:_{(circumference)}+Circle\:_{(diameter)}}[/tex] [tex]\tt{\implies 2\pi\:r+2r=116}[/tex] [tex]\tt{\implies 2r(\pi+1)=116}[/tex] [tex]\tt{\implies 2r(\frac{22}{7}+1)=116}[/tex] [tex]\tt{\implies r(\frac{22+7}{7})=116\div\:2}[/tex] [tex]\tt{\implies \dfrac{29r}{7}=58}[/tex] [tex]\tt{\implies r=7\times\:2}[/tex] [tex]\tt{\implies r=14\:cm}[/tex] [tex]\sf\large{Hence,}[/tex] [tex]\bf{\implies Radius\:of\:_{(circle)}=14\:cm}[/tex] Reply
Question :
The sum of the circumferences and diameter of a circle is 116cm . Find its radius.
Formulas :
●Circumference of circle = 2πr
●Diameter of circle = 2r
Solution :
Circumference + diameter = 116
[tex] \tt \implies [/tex] 2πr + 2r = 116
[tex] \tt \implies [/tex] 2r(π+1) =116
[tex] \tt \implies [/tex] r([tex] \tt \frac{22}{7}[/tex] + 1 ) = [tex] \tt \frac{116}{2}[/tex]
[tex] \tt \implies [/tex] r([tex]\tt \frac{22+7}{7}[/tex]) = 58
[tex] \tt \implies [/tex] r = 58 × [tex] \tt \frac{7}{29}[/tex]
[tex] \tt \implies [/tex] r = 2 × 7
[tex] \tt \implies [/tex] r = 14 cm
[tex] \tt \therefore [/tex] Radius of circle is 14 cm
[tex]\sf\small\underline\red{Given:-}[/tex]
[tex]\sf{\implies Sum\:_{(circumference+diameter)}=116}[/tex]
[tex]\sf\small\underline\red{To\: Find:-}[/tex]
[tex]\sf{\implies Radius\:of\:_{(circle)}=?}[/tex]
[tex]\sf\small\underline\red{Solution:-}[/tex]
By applying formula to calculate the radius of circle as we know that diameter of circle is 2r and circumference of circle is 2πr.
[tex]\sf\small\underline\red{Formula\:used:-}[/tex]
[tex]\sf\longrightarrow{Circumference\:_{(circle)}=2\pi\:r}[/tex]
[tex]\sf\longrightarrow{Diameter\:_{(circle)}=2r}[/tex]
[tex]\bf{\implies Circle\:_{(circumference)}+Circle\:_{(diameter)}}[/tex]
[tex]\tt{\implies 2\pi\:r+2r=116}[/tex]
[tex]\tt{\implies 2r(\pi+1)=116}[/tex]
[tex]\tt{\implies 2r(\frac{22}{7}+1)=116}[/tex]
[tex]\tt{\implies r(\frac{22+7}{7})=116\div\:2}[/tex]
[tex]\tt{\implies \dfrac{29r}{7}=58}[/tex]
[tex]\tt{\implies r=7\times\:2}[/tex]
[tex]\tt{\implies r=14\:cm}[/tex]
[tex]\sf\large{Hence,}[/tex]
[tex]\bf{\implies Radius\:of\:_{(circle)}=14\:cm}[/tex]