Question

the height of acylinder is 40 cm and the circumference of the base is 132cm find the volume of the cylinder and it's lateral surface area?​

Answer 1

Given

• Circumference of the base = 132cm
• Height of cylinder = 40cm

To Find

• Volume of the cylinder
• Lateral surface area

Formula Used

$\: \: \: \: \: \: \:\underline{ \underline{ \boxed{ \gray{ \sf \: Volume \: of \: Cylinder= πr²h}}}}$

$\: \: \: \: \: \: \: \underline{ \underline{ \boxed{ \gray{ \sf \ Lateral \: surface \: Area \: Of \: Cylinder= 2πrh}}}}$

Solution

First We find Radius

$\pink{ \sf \: Circumference \: of \: base= 2πr}$

$\implies\sf \: 132= 2 \times \dfrac{22}{7} \times r$

$\implies\sf \: r = \dfrac{ 132 \times7 }{22 \times 4}$

$\implies\sf \: r = \dfrac{ 924 }{88}$

$~~~~\sf \: r =10.5cm$

$\green{ \sf \: Volume \: of \: Cylinder= πr²h}$

${ \implies \sf \: Volume \: of \: Cylinder= \dfrac{22}{7} \times (10.5) ^{2} \times 40 }$

${ \implies \sf \: Volume \: of \: Cylinder= \dfrac{22}{7} \times 110.25 \times 40 }$

${ \implies \sf \: Volume \: of \: Cylinder= {22} \times 15.75 \times 40 }$

${ \implies \sf \: Volume \: of \: Cylinder= {22} \times 630 }$

$\gray{ \: \:~~~~ \: \: \: \sf \: Volume \: of \: Cylinder= 13860 {cm}^{3} }$

Now we will Find

Lateral surface Area Of Cylinder

$\blue{\sf \ Lateral \: surface \: Area \: Of \: Cylinder= 2πrh}$

${ \implies\sf \ Lateral \: surface \: Area \: Of \: Cylinder= 2πrh}$

${ \implies\sf \ Lateral \: surface \: Area \: Of \: Cylinder= 2 \times \dfrac{22}{7} \times 10.5 \times 40}$

${ \implies\sf \ Lateral \: surface \: Area \: Of \: Cylinder= 2 \times 22 \times 1.5 \times 40}$

${ \implies\sf \ Lateral \: surface \: Area \: Of \: Cylinder=66 \times 40}$

$\gray{ \: \: \: \: \: \sf \ Lateral \: surface \: Area \: Of \: Cylinder = 2640 {cm}^{2} }$

• Volume of Cylinder= 13860cm³
• Lateral surface Area=2540cm²