CSA and volume of cylinder are 2640cm² and 27720³ respectively find radius, height and TSA

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1 thought on “CSA and volume of cylinder are 2640cm² and 27720³ respectively find radius, height and TSA<br /><br />​”

1. [tex]\bf\purple{QuestioN:-}[/tex]

   CSA and volume of cylinder are 2640 cm² and 27720 cm³ respectively. Find radius, height and TSA.

   
   

   [tex]\bf\green{AnsweR:-}[/tex]

   CSA of the cylinder = 2640 cm²​
   

   CSA = 2π × r × h

   Volume of the cylinder = 27720 cm³

   Volume = πr²h

   We need to find,

   r, h & TSA

   ⇒ CSA = 2π × r × h

   ⇒ 2,640 cm² = 2 × 22/7 × r × h

   [tex]\implies\bf{\dfrac{2,640\times7}{2\times22}=r\times{h}}[/tex]

   [tex]\implies\bf{420=r\times{h}}[/tex]

   ⇒ Volume = πr²h

   ⇒ 27,720 cm³ = 22/7 × r² × h

   [tex]\implies\bf{\dfrac{27,720\times7}{22}=r^2\times{h}}[/tex]

   [tex]\implies\bf{8,820=r^2\times{h}}[/tex]

   Now we got,

   [tex]:\longrightarrow\bf{r\times{h}=420}[/tex]

   [tex]:\longrightarrow\bf{r^2\times{h}=8,820}[/tex]

   [tex]:\longrightarrow\bf{r\times{r}\times{h}=8,820}[/tex]

   We already know that, r × h = 420

   Then,

   [tex]:\longrightarrow\bf{r\times420=8,820}[/tex]

   [tex]:\longrightarrow\bf{r=\dfrac{8,820}{420}}[/tex]

   [tex]:\longrightarrow\bf{r=21}[/tex]

   Now we can substitute 21 instead of r in the equation r × h .

   ⇒ r × h = 420

   ⇒ 21 × h = 420

   ⇒ h = 420/21

   ⇒ h = 20.

   Now we got ,

   r = 21

   h = 20

   Then now we can find TSA of the cylinder.

   TSA = 2πr (h + r)

   Now we can substitute the values.

   [tex]\bf{TSA=2\times\dfrac{22}{7}\times(20+21)}[/tex]

   [tex]\bf{TSA=\dfrac{44}{7}\times(41)}[/tex]

   [tex]\bf{TSA=\dfrac{44\times41}{7}}[/tex]

   [tex]\bf{TSA=\dfrac{1804}{7}}[/tex]

   [tex]\bf{TSA=257.71}[/tex]

   Radius = 21 cm

   Height = 20 cm

   TSA = 257 .71 cm²

   Happy Learning !!☺

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