Question

the radius and height of a cylinder are in ratio 5 :7 and its volume is 550 cm³ find its radius and height​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• The radius and height of a cylinder are in ratio 5 :7 and its volume is 550 cm³. find its radius and height

$\large\underline{ \underline{ \sf \maltese{ \: Diagram:- }}}$

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{5cm}}\put(9,17.5){\sf{7cm}}\end{picture}$

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

• Let the Radius be 5x
• Let the Height be 7x

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Volume \: of \: Cyclinder \: = \: \pi \: {r}^{2} h }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{550 \: = \: \frac{22}{7} \: \times \: (5x)^{2} \: \times \: 7x}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{550 \: = \: \frac{22}{\cancel{7}} \: \times \: (5x)^{2} \: \times \: \cancel{7}x}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{550 \: = \: {22} \: * \: 5x \: * \: 5x \: * \: x}}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ 550 \: = \: 550 {x}^{3} }}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ \cancel\frac{550}{550} \: = \: {x}^{3} }}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ 1cm^{3} \: = \: {x} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 1cm }}}$

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• Radius = 5x = 5 × 1 = 5cm
• Height = 7x = 7 × 1 = 7cm

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$\bf \therefore \; Radius \;= 5cm$

$\bf \therefore \; Height\;= 7cm$

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More For Knowledge:-

• A cylinder is called right cylinder if the axis of the cylinder is perpendicular to its base.
• The solid shapes that have curved surfaces with circular and such solids are called right circular cylinders.

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Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question⤵ }}}$

The radius and height of a cylinder are in ratio 5:7 and its volume is 550 cm³. find its radius and height.

❇Solution ⬇

Let the radius of the base and height of the cylinder be 5x cm and 7x cm respectively.

Then,

Volume = 550 cm3

⇒ 22/7 × (5x)2 × 7x = 550 [Use, r = 5x; h = 7x and volume = πr2h]

⇒ 22/7 × 25x² × 7x = 550

⇒ 22 × 25x³ = 550

⇒ 550x³ = 550

⇒ x³ = 1

⇒ x = 1 cm

Hence, radius of the cylinder

= 5x cm = (5 × 1) cm

= 5 cm.

Thank you.