Question

find the curved surface area total surface area and volume of a cylinder with a diameter 7 cm and height 5 cm .pie 22/7​

Answer 1

Given :

$\diamond \rm \: Diameter = 7 \: cm$

$\diamond \rm \: Height = 5 \: cm$

To Find :

$\rm (i) \: \: Curved \: Surface \: Area$

$\rm (ii)Total \: Surface \: Area$

$\rm \: (iii)Volume$

Solution:

$\sf \: Radius = \dfrac{7}{2} = 3.5 \: cm$

$\textbf{\underline{\underline{Curved\:Surface\:Area : }}}$

$\star \tt \: C.S.A = 2\pi \: r \: h$

$\hookrightarrow \sf \: 2 \times \dfrac{22}{7} \times 3.5 \times 5$

$\hookrightarrow \sf \: \dfrac{770}{7}$

$\sf \: C.S.A = \large \boxed{\sf \: 110 \: {cm}^{2} }$

$\textbf{\underline{\underline{Total\:Surface\:Area : }}}$

$\star \tt \: T.S.A = 2\pi \: r(r + h)$

$\hookrightarrow \sf \: 2 \times \dfrac{22}{7} \times 3.5 \: (3.5 + 5)$

$\hookrightarrow \sf \: 2 \times \dfrac{22}{7} \times 3.5 \times 8.5$

$\hookrightarrow \sf \: \dfrac{1309}{7}$

$\sf \: T.S.A = \large \boxed{\sf \: 187 \: {cm}^{2} }$

$\textbf{\underline{\underline{Volume: }}}$

$\star \rm \: Volume = \pi {r}^{2} h$

$\hookrightarrow \sf \: \dfrac{22}{7} \times 3.5 \times 3.5 \times 5$

$\hookrightarrow \sf \dfrac{1347.5}{7}$

$\sf \: Volume= \large \boxed{\sf \: 192.5 \: {cm}^{3} }$

Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\purple{ANSWER\::}}}}}}$

$\bf{Given\begin{cases}\sf{The\:diameter\:of\:cylinder\:(d)\:=\:7cm}\\ \sf{The\:height\:of\:cylinder\:(h)\:=\:5cm}\\ \sf{The\:value\:of\:pie\:=\:\frac{22}{7} }\end{cases}}$

$\bf{\Large{\underline{\bf{To\:Find\::}}}}$

• The curved surface area of cylinder.
• The total surface area of cylinder.
• The volume of a cylinder.

$\bf{\Large{\underline{\boxed{\rm{\green{Explanation\::}}}}}}$

We have,

$\leadsto\rm{Diameter\:=\:7cm}$

$\leadsto\rm{Radius\:=\:\frac{Diameter}{2} }$

$\leadsto\rm{Radius\:(r)\:=\:\frac{7}{2} cm}$

• $\sf{\Large{\boxed{\sf{\blue{1.Volume\:of\:cylinder\::}}}}}$

$\longmapsto\rm{Volume\:=\:\pi r^{2} h}$

$\longmapsto\rm{Volume\:=\:(\frac{22}{7} *\frac{7}{2}*\frac{7}{2} *5)cm^{3} }$

$\longmapsto\rm{Volume\:=\:(\frac{\cancel{22}}{\cancel{7}} *\frac{\cancel{7}}{\cancel{2}}*\frac{7}{2} *5)cm^{3} }$

$\longmapsto\rm{Volume\:=\:(11*\frac{7}{2} *5)cm^{3} }$

$\longmapsto\rm{Volume\:=\:\cancel{(\frac{385}{2} )}cm^{3} }$

$\longmapsto\rm{\red{Volume\:=\:192.5cm^{3} }}}$

• $\sf{\Large{\boxed{\sf{\blue{2.Curved\:surface\:area\:of\:cylinder\::}}}}}$

$\longmapsto\rm{C.S.A.\:=\:2\pi r h}$

$\longmapsto\rm{C.S.A.\:=\:(2*\frac{22}{7} *\frac{7}{2} *5)cm^{2} }$

$\longmapsto\rm{C.S.A.\:=\:(\cancel{2}*\frac{22}{\cancel{7}} *\frac{\cancel{7}}{\cancel{2}} *5)cm^{2} }$

$\longmapsto\rm{C.S.A.\:=\:(22*5)cm^{2} }$

$\longmapsto\rm{\red{C.S.A.\:=\:110cm^{2}}}} }$

• $\sf{\Large{\boxed{\sf{\blue{3.Total\:surface\:area\:of\:cylinder\::}}}}}$

$\longmapsto\rm{T.S.A.\:=\:2\pi r(r+h)}$

$\longmapsto\rm{T.S.A.\:=\:[2*\frac{22}{7} *\frac{7}{2} (\frac{7}{2} +5)]cm^{2} }$

$\longmapsto\rm{T.S.A.\:=\:[\cancel{2}*\frac{22}{\cancel{7}} *\frac{\cancel{7}}{\cancel{2}} (\frac{7}{2} +5)]cm^{2} }$

$\longmapsto\rm{T.S.A.\:=\:[22*(\frac{7+10}{2} )]cm^{2} }$

$\longmapsto\rm{T.S.A.\:=\:(22*(\frac{17}{2} )cm^{2} }$

$\longmapsto\rm{T.S.A.\:=\:\cancel{\frac{374}{2} }cm^{2} }$

$\longmapsto\rm{\red{T.S.A.\:=\:187cm^{2}}}$