Question

# Quality Question
@ Surface Are And Volumes

A right circular cylinder with base radius 14 cm, height 35 cm​,
Find the volume, CSA, TSA of right circular cylinder.​

Answer 1

Given :-

• Radius = 14cm
• Height = 35cm

To Find :-

• Volume of a right circular cylinder
• CSA of a right circular cylinder
• TSA of a right circular cylinder

Formula Used :-

• $volume = \pi \: {r}^{2}h$
• $TSA =2\pi \: r(h + r)$
• $CSA = 2\pi \: rh$

Solution :-

For volume, Substituting the values we get,

$= > \frac{22}{7} \times ({14})^{2} \times 35 \\ = > 22 \times 196 \times 5 \: \: \: \: \: \\ = > 21560 \: {cm}^{3} \: \: \: \: \: \: \: \: \: \:$

For TSA, Substituting the values we get,

$= > 2 \times \frac{22}{7} \times 14(14 + 35) \\ = > 88 \times 49 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > 4312 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

For CSA, Substituting the values we get,

$= > 2 \times \frac{22}{7} \times 14 \times 35 \\ = > 88 \times 35 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > 3080 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore :-

• TSA of the right circular cylinder = 4312 cm²
• CSA of the right circular cylinder = 3080 cm²
• Volume of the right circular cylinder = 21560 cm³

________________________________

Hope it helps you mate :)

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

A right circular cylinder has base radius 14 cm, height 35 cm . Find the volume , CSA ( Curved Surface Area ) , TSA ( Total Surface Area ) of right circular cylinder .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

• Volume of cylinder = $\sf21560\:{cm}^{3}$

• CSA of cylinder = $\sf3080\:{cm}^{2}$

• TSA of cylinder = $\sf4312\:{cm}^{2}$

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• Radius of right circular cylinder ( r )= 14 cm

• Height of right circular cylinder ( h )= 35 cm

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• Volume of right circular cylinder

• CSA of right circular cylinder

• TSA of right circular cylinder

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED: }}}}$

$\purple{ \boxed{ \begin{array}{l} \textsf{Volume of cylinder = \sf\pi {r}^{2}h } \\ \\ \textsf{CSA of cylinder = \sf2\pi rh } \\ \\ \textsf{TSA of cylinder = \sf2\pi r(h + r) } \end{array}}}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

$\red{ \underline{\underline{\textsf{Volume of cylinder : }}}}$

$\displaystyle \longrightarrow \textsf{Volume of cylinder } \sf = \frac{22}{ \cancel7} \times {(14)}^{2} \times \cancel{35} { \: \: }^{5} \: \\ \\ \displaystyle \longrightarrow \textsf{Volume of cylinder } \sf =22 \times 196 \times 5 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{Volume of cylinder } \sf =21560 \: {cm}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\red{ \underline{\underline{\textsf{CSA of cylinder : }}}}$

$\displaystyle \longrightarrow \textsf{CSA of cylinder } \sf = 2 \times \frac{22}{ \cancel7} \times 14 \times \cancel{35} { \: \: }^{5} \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{CSA of cylinder } \sf = 2 \times 22 \times 14 \times 5\: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{CSA of cylinder } \sf =3080 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\red{ \underline{\underline{\textsf{TSA of cylinder : }}}}$

$\displaystyle \longrightarrow \textsf{TSA of cylinder } \sf = 2 \times \frac{22}{ \cancel7} \times \cancel{14} { \: \: }^{2} \: (35 + 14) \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf = 2 \times 22 \times 2 \times 49\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf =4312 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \begin{array}{l} \textsf{Volume of cylinder = \sf21560 \: {cm}^{3} } \\ \\ \textsf{CSA of cylinder = \sf3080 \: {cm}^{2} } \\ \\ \textsf{TSA of cylinder = \sf4312 \: {cm}^{2} } \end{array}}}$