Question

Find the height of the cylinder whose volume is 1.54 m and diameter of the base is 140 cm ?​

Answer 1

Answer:

Diagram :

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{0.7\ m}}\put(9,17.5){\sf{1\ m}}\end{picture}$

The diagram of cylinder is given above. See this latex diagram on website Brainly.in.

$\begin{gathered}\end{gathered}$

Given :

• Volume of cylinder = 1.54 m
• Diameter of cylinder = 140 cm.

$\begin{gathered}\end{gathered}$

To Find :

• Radius of cylinder
• Height of cylinder

$\begin{gathered}\end{gathered}$

Using Formula :

$\longrightarrow{\small{\underline{\boxed{\sf{Radius = \dfrac{Diameter}{2} }}}}}$

$\longrightarrow{\small{\underline{\boxed{\sf{Volume \: of \: cylinder = \pi{r}^{2}h}}}}}$

• π = 22/7
• r = radius
• h = height

$\begin{gathered}\end{gathered}$

Solution :

Finding the radius of cylinder by substituting the values in the formula :-

$\longrightarrow \: \: {\sf{Radius = \dfrac{Diameter}{2}}}$

$\longrightarrow \: \: {\sf{Radius = \dfrac{140}{2}}}$

$\longrightarrow \: \: {\sf{Radius = \cancel{\dfrac{140}{2}}}}$

$\longrightarrow \: \: {\sf{Radius =70 \: cm}}$

Coverting radius of cylinder 70 cm to m.

$\longrightarrow \: \: {\sf{Radius =70 \: cm}}$

$\longrightarrow \: \: {\sf{Radius = \dfrac{70}{100} \: m}}$

$\longrightarrow \: \: {\sf{Radius = \cancel{\dfrac{70}{100}}\: m}}$

$\longrightarrow \: \: {\sf{Radius = {\dfrac{7}{10}}\: m}}$

$\longrightarrow \: \: {\sf{Radius = 0.7\: m}}$

$\bigstar \: \purple{\underline{\boxed{\sf{Radius = 0.7\: m}}}}$

Hence, the radius of cylinder is 0.7 m.

$\rule{300}{1.5}$

Now, according to the question;-

$\longrightarrow \: \:{\sf{Volume \: of \: cylinder = \pi{r}^{2}h}}$

$\longrightarrow \: \:{\sf{1.54= \dfrac{22}{7} \times {(0.7)}^{2} \times h}}$

$\longrightarrow \: \:{\sf{1.54= \dfrac{22}{7} \times {(0.7 \times 0.7)}\times h}}$

$\longrightarrow \: \:{\sf{1.54= \dfrac{22}{7} \times {(0.49)}\times h}}$

$\longrightarrow \: \:{\sf{1.54= \dfrac{22}{7} \times 0.49\times h}}$

$\longrightarrow \: \:{\sf{1.54= \dfrac{22}{\cancel{7}} \times \cancel{0.49}\times h}}$

$\longrightarrow \: \:{\sf{1.54= 22\times 0.7\times h}}$

$\longrightarrow \: \:{\sf{1.54= 1.54\times h}}$

$\longrightarrow \: \:{\sf{1.54= 1.54h}}$

$\longrightarrow \: \:{\sf{h = \dfrac{1.54}{1.54}}}$

$\longrightarrow \: \:{\sf{h = \cancel{\dfrac{1.54}{1.54}}}}$

$\longrightarrow \: \:{\sf{h = 1 \: m}}$

$\bigstar \: \purple{\underline{\boxed{\sf{Height= 1\: m}}}}$

Hence, the height of cylinder is 1 m.

$\begin{gathered}\end{gathered}$

Vefication :

Let's check our answer by substituting all values in the formula :-

$\longrightarrow \: \:{\sf{Volume \: of \: cylinder = \pi{r}^{2}h}}$

$\longrightarrow \: \:{\sf{1.54 \: m= \dfrac{22}{7} \times {(0.7)}^{2} \times 1}}$

$\longrightarrow \: \:{\sf{1.54 \: m = \dfrac{22}{7} \times {(0.7 \times 0.7)}\times 1}}$

$\longrightarrow \: \:{\sf{1.54 \: m = \dfrac{22}{7} \times {(0.49)}\times 1}}$

$\longrightarrow \: \:{\sf{1.54 \: m = \dfrac{22}{7} \times 0.49\times 1}}$

$\longrightarrow \: \:{\sf{1.54 \: m = \dfrac{22}{\cancel{7}}\times \cancel{0.49}\times 1}}$

$\longrightarrow \: \:{\sf{1.54 \: m = 22\times 0.7\times 1}}$

$\longrightarrow \: \:{\sf{1.54 \: m = 22\times 0.7}}$

$\longrightarrow \: \:{\sf{1.54 \: m = 1.54 \: m}}$

$\bigstar \: \purple{\underline{\boxed{\sf{LHS = RHS}}}}$

$\begin{gathered}\end{gathered}$

Learn More :

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

$\rule{220pt}{3pt}$

Answer 2

Question :-

Find the height of the cylinder whose volume is 1.54 m and diameter of the base is 140 cm ?

Answer :-

• The height of cylinder is 1m.

Step by step explanation :-

In the question we have asked to find the height of cylinder and we have given that is volume of that cylinder is 1.54m $^{3}$ and the diameter of the base is 140cm.

Method of solving :

First we have to convert the diameter into m $( \because$ the diameter is in cm). Then we have to find radius using diameter, and we use the volume formula of cylinder put the having values and find height of that cylinder.

We know that,

$\longrightarrow$ 1m = 100cm

Then,

$\longrightarrow$ 140m = 1.4m

Also we know that,

$\longrightarrow$ Radius = $\frac{\rm Diameter}{2}$

According to the formula,

$\longrightarrow$ Radius = $\frac{1.4}{2}$ = 0.7m

Using formula,

$\hookrightarrow$ Volume = $\pi$ r²h

Substituting the values,

$\rm:\longmapsto{1.54 = \frac{ 22 }{7} \times (0.7) {}^{2} \times h } \\ \\ \rm:\longmapsto{1.54 = \frac{22}{ \cancel7} \times \cancel{ 0.49} \times h } \: \: \: \: \\ \\ \rm:\longmapsto{1.54 =22 \times 0.07 \times h } \: \: \: \: \: \\ \\ \rm:\longmapsto{1.54 = 1.54 \times h} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{h = \cancel\frac{1.54}{1.54} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto \red{height = \boxed{\rm{{1m}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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