Question

find the curved surface area,total surface area,and volume of cylinder with the radius 20cm and hieght 42cm​

Answer 1

Given: The value of radius and height of the Cylinder is 20 cm and 42 cm respectively.

Need to find: The CSA, TSA & Volume of Cylinder?

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✇ We've radius and Height of cylinder. Formula to find Volume of Cylinder is Given by —

$\star\:\underline{\boxed{\pmb{\sf{Volume_{ \: (Cylinder)} = \pi r^2 h}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{By\:putting\:values\:in\:formula\::}}}\\\\\\ \dashrightarrow\sf Volume_{\:(cylinder)} = \bigg(\dfrac{22}{7}\bigg)\times \Big(20\Big)^2 \times 42\\\\\\ \dashrightarrow\sf Volume_{\:(cylinder)} = \dfrac{22}{\cancel{\;7}} \times 400 \times \cancel{42}\\\\\\ \dashrightarrow\sf Volume_{\:(cylinder)} = 22 \times 400 \times 6\\\\\\ \dashrightarrow\sf Volume_{\:(cylinder)} = 22 \times 2400\\\\\\ \dashrightarrow\underline{\boxed{\pmb{\frak{\mathcal{V}olume_{\:(cylinder)} = 52800\:cm^3}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \: Volume\:of\:cylinder\:is\:{\pmb{\sf{52800\;cm^3}}}.}}}$

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✇ Now, we'll find TSA(Total Surface Area) of Cylinder, To find TSA of Cylinder formula is Given by —

$\qquad\star\:\underline{\boxed{\pmb{\sf{Total\;Surface\;Area_{ \: (Cylinder)} = 2\pi r(r +h)}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{By\:putting\:values\:in\:formula\::}}}\\\\\\ \dashrightarrow\sf TSA_{\:(cylinder)} = 2 \times \bigg(\dfrac{22}{7}\bigg)\times 20 \Big(20 + 42\Big)\\\\\\ \dashrightarrow\sf TSA_{\:(cylinder)} = \dfrac{44}{7} \times 20 \times \Big(62\Big)\\\\\\ \dashrightarrow\sf TSA_{\:(cylinder)} = \dfrac{44}{7} \times 1240\\\\\\ \dashrightarrow\sf TSA_{\:(cylinder)} =\cancel \dfrac{54560}{7}\\\\\\ \dashrightarrow\underline{\boxed{\pmb{\frak{TSA_{\:(cylinder)} = 7794.28\;(approx)}}}}\;\bigstar$

⠀⠀$\therefore{\underline{\sf{Hence, \;TSA\:of\:cylinder\:is\:{\pmb{\sf{7794.28\;cm^2}}}.}}}$

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✇ Aslo, we've to find CSA (Curved Surface Area) of Cylinder. To find CSA of Cylinder formula is Given by —

$\qquad\star\:\underline{\boxed{\pmb{\sf{Curved\;Surface\;Area_{ \: (Cylinder)} = 2\pi rh}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{By\:putting\:values\:in\:formula\::}}}\\\\\\ \dashrightarrow\sf CSA_{\:(cylinder) }= 2 \times \dfrac{22}{7} \times 20 \times 42\\\\\\ \dashrightarrow\sf CSA_{\:(cylinder)} = \dfrac{44}{\cancel{\;7}} \times 20 \times \cancel{42}\\\\\\ \dashrightarrow\sf CSA_{\:(cylinder)} =44 \times 20 \times 6\\\\\\ \dashrightarrow\sf CSA_{\:(cylinder)} = 44 \times 120 \\\\\\ \dashrightarrow\underline{\boxed{\pmb{\frak{CSA_{\:(cylinder)} = 5280\:cm^2}}}}\;\bigstar$

⠀⠀$\therefore{\underline{\sf{Hence, \;CSA\:of\:cylinder\:is\:{\pmb{\sf{5280\;cm^2}}}.}}}$

Answer 2

Given :-

Radius = 20 cm

Height = 42 cm

To Find :-

CSA

TSA

Volume

Solution :-

1] CSA

CSA of cylinder = 2πrh

⇒ CSA = 2 × 22/7 × 20 × 42

⇒ CSA = 44/7 × 20 × 42

⇒ CSA = 44 × 20 × 6

⇒ CSA = 880 × 6

⇒ CSA = 5280 cm²

2] TSA

⇒ TSA = 2πr(r + h)

⇒ TSA = 2 × π × 20(20 + 42)

⇒ TSA = 40π × 62

⇒ TSA = 1860π cm²

3] Volume

Volume = πr²h

⇒ Volume = 22/7 × (20)² × 42

⇒ Volume = 22/7 × 400 × 42

⇒ Volume = 22 × 400 × 6

⇒ Volume = 52800 cm³