Question

csa,tsa , volume of a cylinder whose height is 1.4 and base radius is 80cm. pls ans quickly

Answer 1

APPROPRIATE QUESTION:-

• Find the CSA, TSA and Volume of a cylinder whose height is 1.4 m and base radius is 80 cm.

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Given:-

• Height of a cylinder = 1.4 m
• Base radius of the cylinder = 80 cm

To find:-

• The Curved Surface Area of the cylinder.
• The Total Surface Area of the cylinder.
• The Volume of the cylinder.

Solution:-

As we are asked to find the CSA, TSA and Volume of the cylinder, first let's recall their formulae!

$\begin{gathered}\boxed{\begin{array}{}\bf { \red{CYLINDER}}\\\frac{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ \bigstar{ \sf{ \: CSA =2\pi rh \: sq.units }}\\ \\ \bigstar{ \sf{ \: TSA = 2\pi r(h + r) \: sq.units}} \\ \\ \bigstar{ \sf{ \: Volume = \pi {r}^{2} h \: cu.units}}\end{array}}\end{gathered}$

If we see the measure given as the height of the cylinder, we can notice that it is in metres while the base radius is in centimetres. So, as first, we shall convert it into centimetres.

We know that, $\small{\boxed{\sf{1\:m=100\:cm}}}$

Henceforth,

$\Rightarrow{\sf{1.4 \:m = 1.4\times 100}}$

$\Rightarrow{\sf{1.4 \:m = \underline{140\:cm}}}$

Now, we shall calculate the required answers!

$\:$

↪CSA of the cylinder:

$\\\:\:\:\:\:\:\:\longmapsto{\textsf{\textbf{\purple{CSA=2 \pi rh\:sq.units}}}}$

• On substituting the measures:

$\\\:\:\:\:\:\:\:\longmapsto{\sf{CSA=\bf{2\times \dfrac{22}{\cancel{7}}\times 80\times \cancel{140}}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{CSA=\bf{2\times 22\times 80\times 20}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{CSA=\bf{44\times 80\times 20}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{CSA=\bf{44\times 1600}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\boxed{\boxed{\bf{CSA=\frak{\red{70,400\:cm^2}}}}}}$

$\:$

↪TSA of the cylinder:

$\\\:\:\:\:\:\:\:\longmapsto{\textsf{\textbf{\purple{TSA = 2 \pi r(h+r)\:sq.units}}}}$

• On substituting the measures:

$\\\:\:\:\:\:\:\:\longmapsto{\sf{TSA=\bf{2\times \dfrac{22}{7}\times 80\times (140+80)}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{TSA=\bf{2\times \dfrac{22}{7}\times 80\times 220}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{TSA=\bf{2\times \dfrac{22}{\cancel{7}}\times \cancel{17600}}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{TSA=\bf{2\times 22\times 2514.28}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{TSA=\bf{44\times 2514.28}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\boxed{\boxed{\bf{TSA=\frak{\red{1,10,628.32\:cm^2}}}}}}$

$\:$

↪Volume of the cylinder:

$\\\:\:\:\:\:\:\:\longmapsto{\textsf{\textbf{\purple{Volume = \pi r ^2 h\:cu.units}}}}$

• On substituting the measures:

$\\\:\:\:\:\:\:\:\longmapsto{\sf{Volume=\bf{\dfrac{22}{7}\times (80)^2\times 140}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{Volume=\bf{\dfrac{22}{7}\times 80\times 80\times 140}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{Volume=\bf{\dfrac{22}{\cancel{7}}\times 6400\times \cancel{140}}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{Volume=\bf{22\times 6400\times 20}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\sf{Volume=\bf{22\times 128000}}}$

$\\\:\:\:\:\:\:\:\longmapsto{\boxed{\boxed{\bf{Volume=\frak{\red{28,16,000\:cm^3}}}}}}$

$\\\therefore{\underline{\sf{The\:CSA,\:TSA\:and\:Volume\:of\:the\:cylinder\:are\:\bf{70,400\:cm^2}\sf ,\:\bf{1,10,628.32\:cm^2}\sf{and}\:\bf{28,16,000\:cm^3}\sf{,\: respectively.}}}}$

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Answer 2

Correct Question-:

• Find Curved surface area, Total Surface Area and Volume of cylinder whose height is 1.4m and base radius is 80cm.

AnswEr-:

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Curved\:Surface\:Area \:of\:Cylinder-:70,400 \:cm^{2} }}}}}}$
• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Total\:Surface\:Area \:of\:Cylinder\:-:1,10,628.32 \:cm^{2} }}}}}}$

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Volume \:of\:Cylinder\:-:28,16,000 \:cm^{3} }}}}}}$

Explanation-:

$\bf{\mathrm { Given -: } }$

• Height of Cylinder is 1.4 m
• Base Radius of Cylinder is 80 cm

$\bf{\mathrm {To\:Find -: } }$

• The Curved Surface Area or CSA of Cylinder.
• The Total Surface Area or TSA of Cylinder.
• Volume of Cylinder.

$\bf{\sf{\dag{ Solution \:for\:Question-:}}}$

• Height of Cylinder is 1.4 m

• [ 1m = 100 cm ]

Then ,

• Height of Cylinder = 1.4 × 100 = 140 cm
• Base Radius of Cylinder is 80 cm

Therefore,

• $\bf{\sf{\purple{Cylinder \:\: -:}}} \begin{cases} \sf{The\:base\:Radius\:of\:Cylinder \:is\: \frak{ 80 \:cm}} & \\\\ \sf{Height \:of\:Cylinder \:is \:\:\frak{140\:cm}}\end{cases}$

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$\bf{\large {\star{\mathrm {\red{ \longrightarrow {Curved \:Surface \:Area\:of\:of\:Cylinder \:-:}}}}}}$

As , We know that ,

• $\boxed{\bf {\dag{\sf {\purple {Curved \:Surface \:Area\:\:of\:Cylinder-:\:2 \:\times \pi \times Radius \times Height \:\: sq.units}}}}}$

Now , By Putting known Values in the Formula-:

• $\bf{\longrightarrow {\mathrm { 2 \times \dfrac{22}{7} \times 80 \times 140 }}}$

• $\bf{\longrightarrow {\mathrm { 2 \times \dfrac{22}{\cancel {7}} \times 80 \times \cancel {140} }}}$

• $\bf{\longrightarrow {\mathrm { 2 \times 22 \times 80 \times 20 }}}$

• $\bf{\longrightarrow {\mathrm { 44 \times 80 \times 20 }}}$

• $\bf{\longrightarrow {\mathrm { 44 \times 1600 }}}$

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Curved\:Surface\:Area \:-:70,400 \:cm^{2} }}}}}}$

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$\bf{\large {\star{\mathrm {\red{ \longrightarrow {Total \:Surface \:Area\:of\:of\:Cylinder \:-:}}}}}}$

As , We know that ,

• $\boxed{\bf {\dag{\sf {\purple {Total \:Surface \:Area\:\:of\:Cylinder-:\:2 \:\times \pi \times Radius ( Height + Radius)\:\: sq.units}}}}}$

Now , By Putting known Values in the Formula-:

• $\bf{\longrightarrow {\mathrm { 2 \times \dfrac{22}{7} \times 80 ( 140+80) }}}$

• $\bf{\longrightarrow {\mathrm { 2 \times \dfrac{22}{7} \times 80 \times 220 }}}$

• $\bf{\longrightarrow {\mathrm { 2 \times \dfrac{22}{7} \times 80 \times 220 }}}$

• $\bf{\longrightarrow {\mathrm { 2 \times \dfrac{22}{7} \times 17600 }}}$

• $\bf{\longrightarrow {\mathrm { 2 \times \dfrac{22}{\cancel {7}} \times \cancel {17600}}}}$

• $\bf{\longrightarrow {\mathrm { 2 \times 22 \times 2514.28 }}}$

• $\bf{\longrightarrow {\mathrm { 44 \times 2514.28 }}}$

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Total\:Surface\:Area \:-:1,10,628.32 \:cm^{2} }}}}}}$

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$\bf{\large {\star{\mathrm {\red{ \longrightarrow {Volume\:of\:Cylinder \:-:}}}}}}$

As , We know that ,

• $\boxed{\bf {\dag{\sf {\purple {Volume\:\:of\:Cylinder-:\: \pi \times Radius^{2} \times Height \:\: cu.units}}}}}$

Now , By Putting known Values in the Formula-:

• $\bf{\longrightarrow {\mathrm { \dfrac{22}{7} \times 80^{2} \times 140 }}}$

• $\bf{\longrightarrow {\mathrm { \dfrac{22}{\cancel {7}} \times 80^{2} \times \cancel {140} }}}$

• $\bf{\longrightarrow {\mathrm { 22 \times 80^{2} \times 20 }}}$

• $\bf{\longrightarrow {\mathrm { 22 \times 80 \times 80 \times 20 }}}$

• $\bf{\longrightarrow {\mathrm { 22 \times 6400 \times 20 }}}$

• $\bf{\longrightarrow {\mathrm { 140800 \times 20 }}}$

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Volume \:-:2816000 \:cm^{3} }}}}}}$

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Hence ,

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Curved\:Surface\:Area \:of\:Cylinder-:70,400 \:cm^{2} }}}}}}$

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Total\:Surface\:Area \:of\:Cylinder\:-:1,10,628.32 \:cm^{2} }}}}}}$

• $\underline{\boxed{\bf{\longrightarrow {\mathrm {\pink{ Volume \:of\:Cylinder\:-:28,16,000 \:cm^{3} }}}}}}$

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