Question

Plzzz solve the problem with explanation​

Answer 1

${\bold{\sf{\underline{Understanding \: the \: question}}}}$

• This question says that there is a metal used in making a hollow cylindrical pipe and it's volume is 748 cm³ Now this question says that it's length is 14 cm and it's external radius is 9 cm. Now it says that we have to find the interior radius of that object.

${\bold{\sf{\underline{Given \: that}}}}$

• Volume of hollow cylindrical pipe = 748 cm³

• ❉Length is 14 cm

• Exterior radius is 9 cm

${\bold{\sf{\underline{To \: find}}}}$

• Interior radius of hollow cylindrical pipe

${\bold{\sf{\underline{Solution}}}}$

• Interior radius of hollow cylindrical pipe = 8 cm

${\bold{\sf{\underline{Assumptions}}}}$

• Let exterior radius is E

• Let interior radius is I

${\bold{\sf{\underline{Using \: concept}}}}$

• Volume of given hollow cylindrical pipe formula ( atq )

${\bold{\sf{\underline{Using \: formula}}}}$

• Volume of given hollow cylindrical pipe = π(E² - I²) × h

${\bold{\sf{\underline{Full \: solution}}}}$

↦ Volume = π(E² - I²) × h

↦ 748 = 22/7 (9² - I²) × 14

↦ 748 = 22 (81 - I²) × 2

↦ 748 = 44 (81 - l²)

↦ 748 / 44 = 81 - l²

↦ 474 / 22 = 81 - l²

↦ 237 / 11 = 81 - I²

↦ 17 = 81 - l²

↦ 81 - 17 = l²

↦ 64 = l²

↦ √64 = l

↦ 8 = l

↦ I = 8 cm

• Henceforth, 8 cm is interior radius of hollow cylindrical pipe.

More knowledge -

Diagram of Cylinder : -

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

Formulas related to Cylinders : -

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

Formulas related to SA & Volume :-

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

Request:-

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Answer 2

Question given :

• There is a cylindrical pipe made with metal . The volume of metal used in making it is 748 cm³ . The length of the pipe is 14 cm and its external radius is 9 cm . We need to find the internal radius .

Given :

• The volume of metal used in making a a cylindrical pipe is 748 cm³
• The length of the pipe is 14 cm
• The external radius of the pipe is 9 cm

To find :

• It's internal radius

Solution :

• Let us take the external radius as Rₑ and the internal radius as Rᵢ .

• We would use here the formula of volume of a hollow cylindrical pipe , That is ,

$\sf\:\implies\: Volume\:=\:\pi(e^2\:-\:i^2)\:\times\:height$

• Note that the given length is the height of the cylinder

As the value of pi is not given we will use 22/7 as it's value in calculating the volume ,

$\sf\:\implies\: Volume\:=\:\pi(e^2\:-\:i^2)\:\times\:height$

$\sf\:\implies\:748\:cm^3\:=\:\dfrac{22}{7}(9^2\:-\:i^2)\:\times\:14$

Seven and fourteen get reduced to their lowest terms which gives out ,

$\sf\:\implies\:748\:cm^3\:=\:22(81\:-\:i^2)\:\times\:2$

Multiply 22 with 2 ,

$\sf\:\implies\:748\:cm^3\:=\:44(81\:-\:i^2)$

Divide 44 by 748 ,

$\sf\:\implies\:\dfrac{748}{44}\:=\:81\:-\:i^2$

Reduce the fraction to its lowest terms ,

$\sf\:\implies\:\dfrac{474}{22}\:=\:81\:-\:i^2$

$\sf\:\implies\:\dfrac{237}{11}\:=\:81\:-\:i^2$

$\sf\:\implies\:17\:=\:81\:-\:i^2$

$\sf\:\implies\:81\:-\:17\:=\:i^2$

$\sf\:\implies\:64\:=\:i^2$

$\sf\:\implies\:\sqrt{64}\:=\:i$

$\sf\:\implies\:8\:=\:i$

Therefore it's internal radius is 8 cm