Question

1. A cylindrical piece of maximum volume has to be
out of an iron cube of edge 4 om. Find
the volume of the cylinder? ​

Answer 1

Answer:-

The volume of the cylinder is 16π cm³

Explanation:-

Given:-

• Edge of the iron cube is 4 cm

To find:-

• volume of the cylinder

Solution:-

Edge of cube = height of the cylinder (h) = 4 cm

Radius of the cylinder (r) = 4/2 cm = 2 cm

We know that,

⠀⠀

⠀⠀⠀⠀${\underline{\boxed{\sf{Volume\:of\:cylinder=πr^{2}h}}}}$

⠀⠀

Now,

Volume of the cylinder = π × (2)² × 4 cm³

Volume of the cylinder = π × 4 × 4 cm³

Volume of the cylinder = 16π cm³

⠀⠀

.°. Volume of the cylinder is 16π cm³

⠀⠀

⠀____________________

⠀⠀

⠀⠀Diagram of a 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 (Cylinder)

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

⠀____________________

Answer 2

$\huge\underline{\bf \red{ ❥ Aɴsᴡᴇʀ }}$

Edge of cube = height of the cylinder (h) = 4 cm

Radius of the cylinder (r) = 4/2 cm = 2 cm

⠀⠀⠀⠀⠀ ❥ Volume of cylinder = πr²h

Now,

=> π × (2)² × 4 cm³

=> π × 4 × 4 cm³

=> 16π cm³⠀⠀

Therefore, the volume of the cylinder is 16π cm³.