Math, asked by ramashankerrathor, 1 year ago

the radius and height of a cylinder are in the ratio of 4:5 and its volume is 2160m. find its daimeter and height​

Answers

Answered by Anonymous
21

\large\underline{\underline{\sf Given:}}

  • Ratio of radius and height of cylinder ( r : h ) = 4 : 5

  • Volume of cylinder (V) = 2160m³

\large\underline{\underline{\sf To\:Find:}}

  • Diameter of cylinder (d) = ?

  • Height of cylinder (h) = ?

\large\underline{\underline{\sf Solution:}}

Let ,

r : h = 4 : 5

r = 4x

h = 5x

As we know,

\large{\boxed{\sf Volume\:Of\: Cylinder (V) = πr^2h}}

\large\implies{\sf 2160=\frac{22}{7}×(4x)^2×5x }

\large\implies{\sf 2160=\frac{22}{7}×80x^3}

\large\implies{\sf x^3=\frac{15120}{1760}}

\large\implies{\sf x=2.04 }

On Putting value of of x :

\large\implies{\sf r=4x }

\large\implies{\sf r=4×2.04 }

\large\implies{\sf r=8.16m }

\large\implies{\sf Diameter=2×8.16m}

\large\implies{\sf D=16. 32m}

\large\implies{\sf h=5x}

\large\implies{\sf h=5×2.04 }

\large\implies{\sf h=10.2m}

\Large\underline{\underline{\sf Answer:}}

•°•Diameter of Cylinder is 16.32m and Height of Cylinder is 10.2m

Answered by Anonymous
113

AnswEr :

  • Ratio of Radius and Height of Cylinder is 4:5.
  • Volume of Cylinder is 2160m³
  • Find Diameter and Height.

Let the Radius be 4x and Height be 5x.

 \boxed{ \bf{Volume  \: of  \: Cylinder = \pi {r}^{2}h  }}

\longrightarrow\sf{Volume = \pi {r}^{2}h}

\longrightarrow\sf{2160 =  \dfrac{22}{7}  \times {(4x)}^{2} \times 5x}

\longrightarrow\sf{ \cancel{2160} =  \dfrac{22}{7}  \times {16x}^{2} \times  \cancel{5}x}

\longrightarrow\sf{432=  \dfrac{22}{7}  \times {16x}^{2} \times x}

\longrightarrow\sf{432 \times 7= 22 \times {16x}^{2} \times x}

\longrightarrow\sf{3024 = 352 {x}^{3} }

 \longrightarrow \sf{  \cancel\dfrac{3024}{352}  =  {x}^{3} }

 \longrightarrow \sf{ \dfrac{189}{22}  =  {x}^{3} }

 \longrightarrow \sf{  \sqrt[3]{\dfrac{189}{22}}  = x }

 \longrightarrow \sf{x =  \dfrac{5.73}{2.80} }

 \longrightarrow  \large\sf{x = 2.04}

━━━━━━━━━━━━━━━━━━━━━━━━

Calculation of Diameter and Height :

⇒ Diameter = 2 × Radius

⇒ Diameter = 2 × ( 4x )

⇒ Diameter = 2 × ( 4 × 2.04 )

⇒ Diameter = 2 × 8.16

Diameter = 16.32 m

⇒ Height = ( 5x )

⇒ Height = ( 5 × 2.04 )

Height = 10.20 m

 \therefore Diameter and Height of Cylinder is 16.32m and 10.2m respectively.

Similar questions