Question

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

Answer 1

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

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

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

• 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

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

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

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

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

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

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

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

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

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

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

Answer 2

Given information,

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

• Radius of base of cylinder = 14 cm
• Height of cylinder = 35 cm
• Volume of cylinder = ?
• C.S.A of cylinder = ?
• T.S.A of cylinder = ?

Using formula,

✪ Volume of cylinder = πr²h ✪

Where,

• π = Pi
• r = radius of base of cylinder
• h = height of cylinder

We have,

• π = 22/7
• r = 14 cm
• h = 35 cm

Putting all values,

➻ Volume of cylinder = 22/7 × 14² × 35

➻ Volume of cylinder = 22/7 × 196 × 35

➻ Volume of cylinder = 22 × 196 × 5

➻ Volume of cylinder = 196 × 110

➻ Volume of cylinder = 21560 cm³

• Henceforth, volume of cylinder is 21560 cm³.

Using formula,

✪ C.S.A of cylinder = 2πrh ✪

Where,

• π = Pi
• r = radius of base of cylinder
• h = height of cylinder

We have,

• π = 22/7
• r = 14 cm
• h = 35 cm

Putting all values,

➻ C.S.A of cylinder = 2 × 22/7 × 14 × 35

➻ C.S.A of cylinder = 2 × 22 × 14 × 5

➻ C.S.A of cylinder = 44 × 70

➻ C.S.A of cylinder = 3080 cm²

• Henceforth, C.S.A of cylinder is 3080 cm².

Using formula,

✪ T.S.A of cylinder = 2πr(r + h) ✪

Where,

• π = Pi
• r = radius of base of cylinder
• h = height of cylinder

We have,

• π = 22/7
• r = 14 cm
• h = 35 cm

Putting all values,

➻ T.S.A of cylinder = 2 × 22/7 × 14(14+35)

➻ T.S.A of cylinder = 2 × 22/7 × 14 × 49

➻ T.S.A of cylinder = 2 × 22 × 14 × 7

➻ T.S.A of cylinder = 44 × 98

➻ T.S.A of cylinder = 4312 cm²

• Henceforth, T.S.A of cylinder is 4312 cm².

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