Question

If the lateral surface of a cylinder is 94.2 cm and its height is 5 cm, then find
(i) radius of its base (ii) its volume. (Use T = 3.14)​

Answer 1

Given:-

• Lateral Surface Area of the cylinder = 94.2 cm²
• Height of the cylinder = 5 cm

To Find:-

• Radius of its base
• Its volume

Note:-

• We need to take the value of π as 3.14 while finding the volume.

Solution:-

We know,

$\boxed{\sf{Lateral\:Surface\:Area\:of\:cylinder = 2\pi rh\:sq.units}}$

Now,

We are given the values of height and Lateral Surface Area,

Hence putting the values in the formula:-

= $\sf{94.2 = 2\times3.14\times r\times 5}$

= $\sf{\dfrac{94.2}{2\times3.14\times 5} = r}$

$\sf{\dfrac{94.2}{3.14} = r}$

=> $\sf{r = 3\:cm }$

(i) Therefore the radius of the base is 3 cm

Now,

We need to find the Volume of the cylinder.

We know,

Volume of the cylinder = πr²h

Hence,

Volume = $\sf{3.14\times (3)^2 \times 5}$

Volume = $\sf{3.14\times 9\times 5}$

Volume = $\sf{141.3\:cm^3}$

Hence the volume of the cylinder is 141.3 cm³.

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Formulas Used:-

• Volume of the cylinder = πr²h cu.units
• Lateral Surface Area of the cylinder = 2πrh sq.units

More Formula:-

• Total Surface Area of the cylinder = 2πr(r + h) sq.units

______________________________________

How Did I Solve:-

Firstly we were given the lateral surface area and the height of the cylinder through which we got an approximate value of radius of the base of the cylinder. The radius of the base came to be 2.99 cm which became 3 cm after rounding off. Then we got the values of height and radius of the base of the cylinder which we put into the formula of the volume of the cylinder, in order to get the volume of the cylinder.

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Answer 2

${\large{\bold{\bf{\sf{\underline{Understanding \; the \; question}}}}}}$

➥ This question says that the lateral surface of a cylinder is 94.2 cm and it's height is 5 cm, then we have to find the following datas –

a. Radius of it's base.

b. It's volume.

And this question also says that we have to use 3.14 at the place of π

${\large{\bold{\bf{\sf{\underline{Given \; that}}}}}}$

➥ The lateral surface area of a cylinder is 94.2 cm

➥ Height of the cylinder is 5 cm

${\large{\bold{\bf{\sf{\underline{To \; find}}}}}}$

➥ Radius of it's base.

➥ It's volume

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

➥ Radius of it's base = 3 cm

➥ It's volume = 141.3 cm³

${\large{\bold{\bf{\sf{\underline{Using \; concepts}}}}}}$

➥ Volume of cylinder formula.

➥ Formula to find lateral surface area of cylinder.

${\large{\bold{\bf{\sf{\underline{Using \; concepts}}}}}}$

➥ Volume of cylinder = πr²h

➥ Lateral surface of cylinder = 2πrh

${\large{\bold{\bf{\sf{\underline{Small \: procedure}}}}}}$

➥ To solve this problem part a. firstly we have to use the formula to find lateral surface area of cylinder afterthat we have to put the values according to that formula. And we get our final result very easily as radius of its base. Now we have to use the formula to find volume of cylinder and putting the values we get our final 6of part b.

${\large{\bold{\bf{\sf{\underline{Full \: Solution}}}}}}$

~ Finding radius of it's base

➨ Lateral surface of cylinder = 2πrh

➨ 94.2 = 2 × 13.4 × r × 5

➨ 94.2 = 26.8 × r × 5

➨ 94.2 = 134 × r

➨ 94.2 / 134 = r

➨ 3 cm (approx) = r

➨ r = 3 cm (approx)

• Henceforth, 3 cm approx us the radius of it's base.

~ Now finding the volume

➨ Volume = πr²h

➨ Volume = 13.4 × 3² × 5

➨ Volume = 13.4 × 3 × 3 × 5

➨ Volume = 13.4 × 9 × 5

➨ Volume = 13.4 × 45

➨ Volume = 141.3 cm³

• Henceforth, 141.3 cm³ is the volume of given cylinder

${\large{\bold{\bf{\sf{\underline{More \: knowledge}}}}}}$

Cylinder diagram

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

Formulas (Cylinder) :

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

Formulas related to SA & Volume :

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

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Request : Please see this answer from web browser or chrome just saying because I give some formulas and diagram here but they are not shown in app

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