Question

the volume of a right circular cylinder is 38016cm3.if the height of the cylinder is 21cm, find it curves surface area?​

Answer 1

Given: The Volume of a right Circular Cylinder is 38016 cm³. & The height of the given right Circular Cylinder is 21 cm.

Need to find: CSA (Curved Surface Area) of Cylinder?

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¤ To Calculate the CSA of Cylinder we'll require the radius of Cylinder. So, Let's find out the radius of Cylinder —

» Formula to find Volume of Cylinder is Given by :

$\quad\star\;\underline{\boxed{\pmb{\frak{ \sf{V}olume_{\:(Cylinder)} = \pi r^2 h}}}}$

⠀⠀⠀$\underline{\bf{\dag} \:\mathfrak{Substituting\;values\;in\; formula\: :}}$⠀⠀⠀⠀

$:\implies\sf 38016 = \dfrac{22}{\cancel{ \: 7}} \times r^2 \times \cancel{21}\\\\\\:\implies\sf 38016 = 22 \times r^2 \times 3\\\\\\:\implies\sf 38016 = 66 \times r^2\\\\\\:\implies\sf r^2 = \cancel\dfrac{38016}{66}\\\\\\:\implies\sf r^2 = 576\\\\\\:\implies\sf r = \sqrt{576}\\\\\\:\implies\underline{\boxed{\pmb{\frak{r = 24}}}}\;\bigstar$

$\:\;\therefore{\underline{\sf{Radius\;(r)\:of\:cylinder\:is\:{\sf{\pmb{24\:cm}}}.}}}$⠀

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✇ Now, By using radius (r) of Cylinder we'll find out the CSA of Cylinder. Formula of CSA (Curved Surface Area) of Cylinder is Given by —

$\quad\star\;\underline{\boxed{\pmb{\sf{Curved\; Surface\;Area_{\:(Cylinder)} = 2 \pi r h }}}}$

⠀⠀⠀$\underline{\bf{\dag} \:\mathfrak{Substituting\;values\;in\; formula\: :}}$⠀⠀⠀⠀

$:\implies\sf CSA = 2 \times \dfrac{22}{7} \times 24 \times 21\\\\\\:\implies\sf CSA = 2 \times \dfrac{22}{ \cancel{\;7}} \times 24 \times \cancel{21}\\\\\\:\implies\sf CSA = 2 \times 22 \times 24 \times 3\\\\\\:\implies\sf CSA = 44 \times 72\\ \\ \\:\implies\underline{\boxed{\pmb{\frak{CSA_{\:(Cylinder)} = 3168\;cm^2}}}}\;\bigstar$

$\:\;\therefore{\underline{\sf{Curved\;Surface\;Area\:\:of\:cylinder\:is\:{\sf{\pmb{3168\:cm^2}}}.}}}$⠀

Answer 2

Answer :

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• Curved surface area of a right circular cylinder is 3168 cm².

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Explanation :

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Given :

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• Volume of a right circular cylinder is 38016cm³.

• Height of a right circular cylinder is 21 cm.

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To Find :

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• Curved surface area of a right circular cylinder?

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Solution :

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⚝ Understanding the Question :

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❏ Here, we have volume and height (h) of a right circular cylinder and we have to find out it's curved surface area (C.S.A).

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❏ Firstly we will calculate it's radius by using formula of volume of cylinder i.e, Volume of cylinder = πr²h.

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❏ Then, by putting all values in formula of Curved surface area of cylinder i.e, Curved surface area of cylinder = 2πrh we will get our required answer.

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⚝ Finding radius (r) of cylinder :

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➥ Volume (cylinder) = πr²h

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➥ 38016 = 22/7 × r² × 21

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After cancelling 21 with 7 in right hand side, we get :

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➥ 38016 = 22 × 3 × r²

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➥ 38016 = 66 × r²

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➥ r² = 38016/66

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➥ r² = 576

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➥ r = √576

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➥ r = √(24 × 24)

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➥ r = 24

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• Therefore, radius of a right circular cylinder is 24 cm.

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⚝ Finding curved surface area (C.S.A) of cylinder :

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➥ C.S.A (cylinder) = 2πrh

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➥ C.S.A (cylinder) = 2 × 22/7 × 24 × 21

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After cancelling 21 with 7 in right hand side, we get :

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➥ C.S.A (cylinder) = 2 × 22 × 24 × 3

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➥ C.S.A (cylinder) = 44 × 72

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➥ C.S.A (cylinder) = 3168

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❏ This is the required answer! $\red{\clubsuit}$

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• Therefore, curved surface area of a right circular cylinder is 3168 cm².

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Explore more :

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⚝ Formulas of volume and area of different shapes :

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$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area\ formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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