Question

5. What length of a solid cylinder 2 cm in diameter must be taken to recasting
hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5mm​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Diameter of solid cylinder = 2 cm

$\:\:$

• Length of hollow cylinder = 16 cm

$\:\:$

• External diameter = 20 cm

$\:\:$

• Thickness = 2.5 mm

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Length of a solid cylinder must be taken to recasting hollow cylinder

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the height of solid cylinder be "h"

$\:\:$

$\underline{\bold{\texttt{Volume of cylinder :}}}$

$\:\:$

➠ πr²h

$\:\:$

• r = $\sf \dfrac { Diameter } { 2 } = \dfrac { 2 } { 2 } = 1$

• h = height of solid cylinder

$\:\:$

➜ π × 1² × h

$\:\:$

➜ πh -------- (1)

$\:\:$

$\underline{\bold{\texttt{Volume of hollow cylinder :}}}$

$\:\:$

➠ $\sf \pi H(R_1^2 – R_2^2 )$ ----- (2)

$\:\:$

• $\sf R_1$ = Outer radius

• $\sf R_2$ = Inner radius

• H = length of hollow cylinder

$\:\:$

Thickness = 2.5 mm = 0.25 cm

$\:\:$

• Inner radius = 10 - 0.25 = 9.75 = $\sf R_2$

• Length of hollow cylinder = 16 = H

• Outer radius = $\sf \dfrac { 20 } { 2 } = 10$ = $\sf R_1$

$\:\:$

$\underline{\bold{\texttt{Putting these values in (2) }}}$

$\:\:$

➠ $\sf \pi H(R_1^2 – R_2^2 )$

$\:\:$

➜ $\sf \pi 16(10^2 – 9.75^2 )$

$\:\:$

➜ $\sf \pi 16(100 – 95.0625 )$

$\:\:$

➜ $\sf \pi 16(4.9375)$ -------- (3)

$\:\:$

〚 As solid cylinder is just recaste into hollow cylinder hence volume of solid cylinder will be equal to volume of hollow cylinder 〛

$\:\:$

$\underline{\bold{\texttt{Thus , (1) = (3)}}}$

$\:\:$

➜ π × h = 16 × π × 4.9375

$\:\:$

➜ h = 16 × 4.9375

$\:\:$

➨ h = 79 cm

$\:\:$

• Hence the height of solid cylinder recasted into hollow cylinder is 79 cm

$\:\:$

Additional information

$\:\:$

• TSA of solid cylinder = 2πrh + 2πr²

• LSA of solid cylinder = 2πrh

• TSA of hollow cylinder = 2π( r1 + r2)( r1 – r2 + h)

• LSA of hollow cylinder = 2πr1h + 2πr2h

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Diameter of solid cylinder = 2 cm

$\:\:$

• Length of hollow cylinder = 16 cm

$\:\:$

• External diameter = 20 cm

$\:\:$

• Thickness = 2.5 mm

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Length of a solid cylinder must be taken to recasting hollow cylinder

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the height of solid cylinder be "h"

$\:\:$

$\underline{\bold{\texttt{Volume of cylinder :}}}$

$\:\:$

➠ πr²h

$\:\:$

r = $\sf \dfrac { Diameter } { 2 } = \dfrac { 2 } { 2 } = 1$

h = height of solid cylinder

$\:\:$

➜ π × 1² × h

$\:\:$

➜ πh -------- (1)

$\:\:$

$\underline{\bold{\texttt{Volume of hollow cylinder :}}}$

$\:\:$

➠ $\sf \pi H(R_1^2 – R_2^2 )$ ----- (2)

$\:\:$

$\sf R_1$ = Outer radius

$\sf R_2$ = Inner radius

H = length of hollow cylinder

$\:\:$

Thickness = 2.5 mm = 0.25 cm

$\:\:$

Inner radius = 10 - 0.25 = 9.75 = $\sf R_2$

Length of hollow cylinder = 16 = H

Outer radius = $\sf \dfrac { 20 } { 2 } = 10$ = $\sf R_1$

$\:\:$

$\underline{\bold{\texttt{Putting these values in (2) }}}$

$\:\:$

➠ $\sf \pi H(R_1^2 – R_2^2 )$

$\:\:$

➜ $\sf \pi 16(10^2 – 9.75^2 )$

$\:\:$

➜ $\sf \pi 16(100 – 95.0625 )$

$\:\:$

➜ $\sf \pi 16(4.9375)$ -------- (3)

$\:\:$

〚 As solid cylinder is just recaste into hollow cylinder hence volume of solid cylinder will be equal to volume of hollow cylinder 〛

$\:\:$

$\underline{\bold{\texttt{Thus , (1) = (3)}}}$

$\:\:$

➜ π × h = 16 × π × 4.9375

$\:\:$

➜ h = 16 × 4.9375

$\:\:$

➨ h = 79 cm

$\:\:$

• Hence the height of solid cylinder recasted into hollow cylinder is 79 cm

$\:\:$

More information

$\:\:$

• TSA of solid cylinder = 2πrh + 2πr²

• LSA of solid cylinder = 2πrh

• TSA of hollow cylinder = 2π( r1 + r2)( r1 – r2 + h)

• LSA of hollow cylinder = 2πr1h + 2πr2h