Question

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

Answer 1

Given :-

• Height and Radius of cylinder are in ratio of 5:7
• Volume of cylinder = 550 cm³

To Find :-

• Measurements of radius and height

Solution :-

Let the height and Radius of cylinder be 7x and 5x respectively.

Volume of cylinder = 550 cm³

$\huge{\boxed{\color{cyan}{Volume\:=\:πr²h}}}$

Where,

• π = $\dfrac{22}{7}$
• h = height of cylinder
• r = Radius of cylinder

Substituting the value in the above formula

$\mapsto{Volume\:=\: \frac{22}{7} \times 5x \times 5x \times 7x }$

$\mapsto{550\:cm³\:=\: \frac{22}{\cancel{7}} \times 5x \times 5x \times {\cancel{7x}}}$

$\mapsto{550\:cm³\:=\: 22 \times 5x \times 5x \times x}$

$\mapsto{550\:cm³\:=\: 550x³}$

$\frac{\cancel{550:cm³}}{\cancel{550}} = x³$

${x}^{3} = 1$

$\huge{\boxed{\mathtt{\blue{x\:=\:1\:cm}}}}$

Measurements of Radius and height are :-

Radius = 5x = 5×1 = 5cm

Height = 7x = 7×1 = 7cm

Hope it helps.......

Answer 2

${\huge{\underline{\underline{\rm{Question:-}}}}}$

Q) The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm³ . Find it's radius and height .

${\huge{\underline{\underline{\rm{Answer\checkmark}}}}}$

★ Given :

• Radius : Height = 5:7
• Volume = 550 cm³

★ To Find :

• Radius = ?
• Height = ?

★ Solution :

Let the ratios be 5x & 7x ,

it means

• Radius = 5x
• Height = 7x

Using the Formula

$\pink\star \: \: \: \: \: \: { \boxed{ \sf{volume _{cyl} = \pi {r}^{2}h }}} \: \: \: \: \: \: \pink\star$

$\mapsto \rm \: \cancel{550 }\: {cm}^{3} = \frac{ \cancel{22}}{ \cancel7} \times {(5x)}^{2} \times \cancel 7x$

$\mapsto \rm \: \cancel{25} \: {cm}^{3} = \cancel{ 25 }{x}^{2} \times x$

$\mapsto \rm \: {x}^{3 } = 1 \: {cm}^{3}$

$\mapsto \rm \: x = \sqrt[3]{1 \: {cm}^{3} }$

$\rightarrow \underline{ \boxed{ \rm{ \purple{x = 1 \: cm}}}}$

So ,

$\rightarrow \rm \: radius = 5x = 5 \times 1 \: cm$

$\rightarrow \underline{ \boxed{ \rm{ \red{radius = 5 \: cm}}}}$

&

$\rightarrow \rm \: height = 7x = 7 \times 1 \: cm$

$\rightarrow \underline{ \boxed{ \rm{ \pink{height = 7 \: cm}}}}$

_________________________

★ Diagram :

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