Question

Find the csa, tsa, and volume of cylinder where height is 8 cm and diameter is 21 cm​​

Answer 1

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

Find the csa, tsa, and volume of cylinder where height is 8 cm and diameter is 21 cm .

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

Volume of cylinder = $\sf2772\:{cm}^{3}$

CSA of cylinder = $\sf528\:{cm}^{2}$

TSA of cylinder = $\sf1221\:{cm}^{2}$

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

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

• Diameter of cylinder ( d )= 21 cm

• Height of right circular cylinder ( h )= 8 cm

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

• Volume of cylinder .

• CSA of cylinder .

• TSA of cylinder .

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

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

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

$\displaystyle \textsf{Radius of cylinder} \sf = \frac{d}{2} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \textsf{Radius of cylinder} \sf = \frac{21}{2} \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \textsf{Radius of cylinder} \sf = 10.5 \: cm \:$

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

$\displaystyle \longrightarrow \textsf{Volume of cylinder } \sf = \frac{22}{7} \times {(10.5)}^{2} \times 8 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{Volume of cylinder } \sf = \frac{22}{7} \times 110.25 \times 8 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{Volume of cylinder } \sf =2772 \: {cm}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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

$\displaystyle \longrightarrow \textsf{CSA of cylinder } \sf = 2 \times \frac{22}{ 7} \times 10.5 \times 8 \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{CSA of cylinder } \sf = \frac{44}{7} \times 84 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{CSA of cylinder } \sf =528 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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

$\displaystyle \longrightarrow \textsf{TSA of cylinder } \sf = 2 \times \frac{22}{ 7} \times 10.5 \: (8 + 10.5) \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf = \frac{44}{7} \times 194.25 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf =1221 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \begin{array}{l} \textsf{Volume of cylinder = \sf2772 \: {cm}^{3} } \\ \\ \textsf{CSA of cylinder = \sf528 \: {cm}^{2} } \\ \\ \textsf{TSA of cylinder = \sf1221 \: {cm}^{2} } \end{array}}}$

Answer 2

Answer :

• Volume of cylinder is 2772 cm³.
• C.S.A of cylinder is 528 cm².
• T.S.A of cylinder is 1221 cm².

Given :-

• Volume of cylinder where height is 8 cm and diameter is 21 cm.

To Find :-

• Volume of cylinder ?
• C.S.A of cylinder ?
• T.S.A of cylinder ?

Solution :-

• Height of cylinder = 8 cm
• Distance of base of cylinder = 21 cm
• Radius of base of cylinder = Diameter/2 = 21/2 cm.

We know that,

• 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 = 21/2 cm
• h = 8 cm

• Putting all values in formula,

➻ Volume of cylinder = 22/7 × (21/2)² × 8

➻ Volume of cylinder = 22/7 × 21/2 × 21/2 × 8

➻ Volume of cylinder = 11 × 3 × 21 × 4

➻ Volume of cylinder = 33 × 84

➻ Volume of cylinder = 2772 cm³

• Hence, volume of cylinder is 2772 cm³.

We know that,

• 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 = 21/2 cm
• h = 8 cm

• Putting all values in formula,

➻ C.S.A of cylinder = 2 × 22/7 × 21/2 × 8

➻ C.S.A of cylinder = 22 × 3 × 8

➻ C.S.A of cylinder = 66 × 8

➻ C.S.A of cylinder = 528 cm²

• Hence, C.S.A of cylinder is 528 cm².

We know that,

• 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 = 21/2 cm
• h = 8 cm

• Putting all values in formula,

➻ T.S.A of cylinder = 2 × 22/7 × 21/2(21/2 + 8)

➻ T.S.A of cylinder = 22 × 3(10.5 + 8)

➻ T.S.A of cylinder = 22 × 3 × 18.5

➻ T.S.A of cylinder = 66 × 18.5

➻ T.S.A of cylinder = 1221 cm²

• Hence, T.S.A of cylinder is 1221 cm².

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