Question

27. A right cicular cylinder has base radius 14 cm and heiht 21 cm. Find (i) Volumeof
cytinder (ii) Curved surface area.

Answer 1

✬ Volume = 12936 cm³ ✬

✬ CSA = 1848 cm³ ✬

Explanation:

Given:

• Measure of base radius of right circular cylinder is 14 cm.
• Measure of height of the same is 21 cm.

To Find:

• What is the volume & curved surface area of the cylinder ?

Solution: As we know that

★ Volume of Cylinder = πr²h cu. units ★

★ CSA of Cylinder = 2πrh sq. units ★

So Let's put all the values in the formula.

• Taking π = 22/7

$\implies{\rm }$ Volume = 22/7 × 14 × 14 × 21

$\implies{\rm }$ 22 × 2 × 14 × 21

$\implies{\rm }$ 22 × 28 × 21

$\implies{\rm }$ 12936 cm³

Hence, the volume of right circular cylinder is 12,936 cm³.

$\implies{\rm }$ CSA = 2 × 22/7 × 14 × 21

$\implies{\rm }$ 44 × 2 × 21

$\implies{\rm }$ 88 × 21

$\implies{\rm }$ 1848 cm²

Hence, the curved surface area of right circular cylinder is 1848 cm².

Answer 2

Given : A right cicular cylinder has base radius 14 cm and hieght 21 cm .

Exigency To Find : (i) Volume of cylinder (ii) Curved surface area of Cylinder.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Given that ,

• Radius ( r ) of the cylinder is 14 cm .
• Height ( h ) of the Cylinder is 21 cm.

⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀Finding Volume of Cylinder :

$\dag\:\:\pmb{ As,\:We\:know\:that\::}\\\\\qquad\maltese\:\:\bf Formula\:for \:Volume\::$

$\qquad \dag\:\:\bigg\lgroup \pmb{\frak{ Volume_{(Cylinder)} \:=\: \pi r ^2 h \: cu.units }}\bigg\rgroup$

⠀⠀⠀⠀⠀Here , r is the Radius of Cylinder, h is the Height of the cylinder & $\sf \pi \:=\:\dfrac{22}{7}\:\:$

$\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: \pi r ^2 h \: \:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: \pi r ^2 h \: \:\\\\\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: \pi \times (14) ^2 \times 21 \: \:\\\\\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: \pi \times 196 \times 21 \: \:\\\\\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: \dfrac{22}{7} \times 196 \times 21 \: \:\\\\\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: \dfrac{22}{\cancel {7}} \times \cancel {196} \times 21 \: \:\\\\\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: 22 \times 28 \times 21 \: \:\\\\\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: 22 \times 588 \: \:\\\\\qquad \dashrightarrow \sf Volume_{(Cylinder)} \:=\: 12936\: \:\\\\\qquad \therefore \pmb{\underline{\purple{\frak{\:Volume_{(Cylinder)} \:=\: 12936\:cm^3 }}} }\:\:\bigstar$

$\qquad\therefore \underline { \sf Hence, \: The \:Volume \:of \:Cylinder \:is \;\bf 12936 \:cm^3 \:}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀Finding Curved Surface Area ( C.S.A ) of Cylinder :

$\dag\:\:\pmb{ As,\:We\:know\:that\::}\\\\\qquad\maltese\:\:\bf Formula\:for \:C.S.A\::$

$\qquad \dag\:\:\bigg\lgroup \pmb{\frak{ C.S.A_{(Cylinder)} \:=\: 2\pi r h \: sq.units }}\bigg\rgroup$

⠀⠀⠀⠀⠀Here , r is the Radius of Cylinder, h is the Height of the cylinder & $\sf \pi \:=\:\dfrac{22}{7}\:\:$

$\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 2\pi r h \: \:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 2\pi r h \: \:\\\\\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 2\times \dfrac{22}{7} \times 14 \times 21 \: \:\\\\\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 2\times \dfrac{22}{\cancel {7}} \times \cancel {14} \times 21 \: \:\\\\\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 2\times 22 \times 2 \times 21 \: \:\\\\\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 44 \times 2 \times 21 \: \:\\\\\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 88 \times 21 \: \:\\\\\qquad \dashrightarrow \sf C.S.A_{(Cylinder)} \:=\: 1848\: \:\\\\\qquad \therefore \pmb{\underline{\purple{\frak{\:C.S.A_{(Cylinder)} \:=\: 1848\:cm^2 }}} }\:\:\bigstar$

$\qquad\therefore \underline { \sf Hence, \: The \:Curved \:Surface \:Area\:of \:Cylinder \:is \;\bf 1848 \:cm^2 \:}$