Question

in a cylindrical pipe the area of the surface are 5 154 square metre and 880 square metre find the radius and the height of the cylinder​

Answer 1

ANSWER :

$\bf{\Large{\underline{\underline{\sf{Given\::}}}}}$

• A cylinder pipe the surface area = 154 m².
• Curved surface area of cylinder = 880 m².

$\bf{\Large{\underline{\underline{\sf{To\:find\::}}}}}$

The radius and the height of the cylinder.

$\bf{\Large{\underline{\underline{\tt{\green{Explanation\::}}}}}}$

$\boxed{\begin{minipage}{6cm}\sf{\large{\underline{\tt{\red{Formula\::}}}}}\\ \\ \sf Area\:of\:circle\:=\:\pi r^{2} \\ \\ \sf Area\: of\:curved\:surface\:area\:=\:2\pi rh \end{minipage}}$

A/q

$|\implies\:\sf{Cylinder\:Pipe\:=\:\pi r^{2} }\\\\\\\\|\implies\sf{154m^{2} \:=\:\frac{22}{7} *r^{2} }\\\\\\\\|\implies\sf{r^{2} \:=\:\dfrac{\cancel{154} *7}{\cancel{22}} }\\\\\\\\|\implies\sf{r^{2} \:=\:(7*7)m^{2} }\\\\\\\\|\implies\sf{r^{2} \:=\:49m^{2} }\\\\\\\\|\implies\sf{r\:=\:\sqrt{49m^{2} } }\\\\\\\\|\implies\sf{\red{r\:=\:7m}}$

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$\longmapsto\sf{C.S.A.\:=\:2\pi r h}\\\\\\\\\longmapsto\sf{880m^{2} \:=\:2*\frac{22}{\cancel{7}} *\cancel{7}*h}\\\\\\\\\longmapsto\sf{880m^{2}\:=\:44*h}\\\\\\\\\longmapsto\sf{h\:=\:\cancel{\dfrac{880m^{2} }{44m}} }\\\\\\\\\longmapsto\sf{\red{h\:=\:20m}}$

Thus,

• Height = 20m
• Radius = 7m.

Answer 2

Answer:

$\bold\green{Radius\: \&\: Height}$ = ${\boxed{\bold{7\: m \: \& \: 20 \: m}}}$

Step-by-step explanation:

Given:-

• Surface area of cylindrical pipe = 154 sq.m
• Curved surface area = 880 sq.m

To find:-

• Radius = ?
• Height = ?

1st case:-

${\boxed{\bold\green{Surface\: area = \pi{r}^{2} }}}$

$\Rightarrow\sf 154 = \pi{r}^{2} \\\\\Rightarrow\sf 154 = \dfrac{22}{7}\times {r}^{2} \\\\\Rightarrow\sf {r}^{2} =\cancel{154} \times \dfrac{7}{\cancel{22}} \\\\\Rightarrow\sf {r}^{2} = 49 \\\\\Rightarrow\sf r =\sqrt{49}\: m \\\\\Rightarrow{\boxed{\bold\green{r = 7 \: m }}}$

$\therefore\bold{Radius (r) = 7 \: m }$

$\rule{300}{1}$

2nd case:-

${\boxed{\bold\purple{CSA = 2\pi r h }}}$

$\Rightarrow\sf 880 = 2 \pi \times 7 \times h \\\\\Rightarrow\sf 880 = 2 \times \dfrac{22}{\cancel{7}}\times \cancel{7} \times h \\\\\Rightarrow\sf 880 = 44 \times h \\\\\Rightarrow\sf h =\cancel{\dfrac{880}{44}} \\\\\Rightarrow{\boxed{\bold\purple{h = 20 \: m }}}$

$\therefore\bold{Height = 20 \: m }$