Question

the total surface area of cylindrical can whose height is equal to the radius of the base is 2464cm2.find its volume.
​

Answer 1

GIVEN:-

• Total surface area of cylinder is 2464 cm  2  .The height and radius of cylinder are equal

TO FIND:

• Find Its Value?

LETS TAKE:-

⇒ Radius of the cylinder be x therefore the height of the cylinder is also x.

TSA of the cylinder =2464 cm  2

SOLUTION:-

→2πr(h+r)=2464 cm²  

→2×22/7×x(x+x)=2464 cm²  

→44/7×x(2x)=2464cm²  

→44/7×2x ²  =2464cm²  

→2x²  =2464/1×7/44

→2x²=56×7

→→2x ² =392

→x²  =392/2

→x² =196

→x=  $\sqrt{196}$

​ → x=14

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Answer 2

Answer:

Given :

• ➝ Total surface area of cylinder = 2464 cm².
• ➝ Height is equal to the radius of the base.

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

To Find :

• ➝ Radius of cylinder
• ➝ Height of cylinder
• ➝ Volume of cylinder

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

Using Formulas :

${\longrightarrow{\small{\underline{\boxed{\sf{TSA \: of \: cylinder = 2\pi r(r + h)}}}}}}$

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

• »» TSA = Total surface area
• »» π = 22/7
• »» r = radius
• »» h = height

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

Solution :

»» We need to find the volume of cylinder but we don't know the radius and height so first we'll find the radius and height.

»» Here, the radius is equal to height. So, let the radius and height be x cm and x cm.

Now, according to the question :

${\twoheadrightarrow{\sf{TSA \: of \: cylinder = 2\pi r(r + h)}}}$

${\twoheadrightarrow{\sf{2464= 2 \times \dfrac{22}{7} \times x(x + x)}}}$

${\twoheadrightarrow{\sf{2464= \dfrac{2 \times 22}{7} \times x \times 2x}}}$

${\twoheadrightarrow{\sf{2464= \dfrac{44}{7} \times 2{x}^{2}}}}$

${\twoheadrightarrow{\sf{2{x}^{2} = 2464 \times \dfrac{7}{44} }}}$

${\twoheadrightarrow{\sf{2{x}^{2} = \cancel{2464} \times \dfrac{7}{\cancel{44}}}}}$

${\twoheadrightarrow{\sf{2{x}^{2} = 56 \times 7}}}$

${\twoheadrightarrow{\sf{2{x}^{2} = 392}}}$

${\twoheadrightarrow{\sf{{x}^{2} = \dfrac{392}{2}}}}$

${\twoheadrightarrow{\sf{{x}^{2} = \cancel{\dfrac{392}{2}}}}}$

${\twoheadrightarrow{\sf{{x}^{2} = 196}}}$

${\twoheadrightarrow{\sf{x = \sqrt{196} }}}$

${\twoheadrightarrow{\sf{\red{x = 14 \: cm }}}}$

• ⌗ Hence, the radius and height of cylinder is 14 cm.

$\rule{200}2$

Now, finding the volume of cylinder by substituting the values in the formula :

${\rightarrow{\sf{Volume_{(Cylinder)} = \pi{r}^{2}h}}}$

${\rightarrow{\sf{Volume_{(Cylinder)} = \dfrac{22}{7} \times {(14)}^{2} \times 14}}}$

${\rightarrow{\sf{Volume_{(Cylinder)} = \dfrac{22}{\cancel{7}} \times \cancel{14} \times 14\times 14}}}$

${\rightarrow{\sf{Volume_{(Cylinder)} = 22 \times 2\times 14\times 14}}}$

${\rightarrow{\sf{Volume_{(Cylinder)} = 22 \times 2\times 14\times 14}}}$

${\rightarrow{\sf{\red{Volume_{(Cylinder)} = 8624 \: {cm}^{3}}}}}$

• ⌗ Hence, the volume of cylinder is 8624 cm³.

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

Learn More :

Here is some formulas related to cylinder. See this latex from website Brainly.in.

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

$\rule{220pt}{4pt}$