Question

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

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Answer 1

$\bf\purple{QuestioN:-}$

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

$\bf\green{AnsweR:-}$

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

$\implies\bf{\dfrac{2,640\times7}{2\times22}=r\times{h}}$

$\implies\bf{420=r\times{h}}$

⇒ Volume = πr²h

⇒ 27,720 cm³ = 22/7 × r² × h

$\implies\bf{\dfrac{27,720\times7}{22}=r^2\times{h}}$

$\implies\bf{8,820=r^2\times{h}}$

Now we got,

$:\longrightarrow\bf{r\times{h}=420}$

$:\longrightarrow\bf{r^2\times{h}=8,820}$

$:\longrightarrow\bf{r\times{r}\times{h}=8,820}$

We already know that, r × h = 420

Then,

$:\longrightarrow\bf{r\times420=8,820}$

$:\longrightarrow\bf{r=\dfrac{8,820}{420}}$

$:\longrightarrow\bf{r=21}$

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.

$\bf{TSA=2\times\dfrac{22}{7}\times(20+21)}$

$\bf{TSA=\dfrac{44}{7}\times(41)}$

$\bf{TSA=\dfrac{44\times41}{7}}$

$\bf{TSA=\dfrac{1804}{7}}$

$\bf{TSA=257.71}$

Radius = 21 cm

Height = 20 cm

TSA = 257 .71 cm²

Happy Learning !!☺