Question

The curved surface area of a cylindrical pillar is 264 m- and its volume is 924 m. Find
the diameter and height of the pillar.​

Answer 1

Answer:

diameter is 14 cm and height is 6cm

Answer 2

$\large \dag$ Question :-

The curved surface area of a cylindrical pillar is 264 m square and its volume is 924 m square.find the diameter and height of the pillar.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Diameter \: of \:  piller\:  is \:14 \: m }} }$

$\red\dashrightarrow\underline{\underline{\sf  \green{Height \: of \:  piller\:  is \:6 \: m }} }$

$\large \dag$ Step by step Explanation :-

❒ We know that curved surface area of cylinder is :-

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{   \blue{CSA = 2\pmb\pi{r}^{}h \:  \:  \: }}}}$

where

r = Radius of base of Cylinder

h = Height of Cylinder

Now here in the question we have,

CSA = 264 m²

⏩ Putting Value in formula ;

$:\longmapsto \rm 264 = 2\pi rh$

$:\longmapsto \rm\pi rh =\cancel \frac{264}{2}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf \pmb\pi rh = 132} }}}----(1)$

❒ Also we know that volume of cylinder is :-

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{   \blue{Volume = \pmb\pi{r}^{2}h \:  \:  \: }}}}$

where

r = Radius of base of Cylinder

h = Height of Cylinder

Now here in the question we have,

Volume = 924 m³

⏩ Putting Value in formula ;

$:\longmapsto \rm 924 = \pi {r}^{2} h$

$:\longmapsto \rm 924 = (\pi rh).r$

✧ Putting Value of $\large \pmb{\sf\pi rh}$

$:\longmapsto \rm 924 = 132 \times r$

$:\longmapsto \rm r = \cancel\frac{924}{132}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf r = 7 \: m} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{Radius \: of \: Piller = 7 \: m}}}}}$

$\therefore\rm Diameter = 2 \times Radius$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{Diameter \: of \: Piller = 14 \: m}}}}}$

⏩ Putting Value of r in in eq (1) :-

$:\longmapsto \rm \pi \times 7 \times h = 132$

$:\longmapsto \rm \frac{22}{ \cancel7} \times \cancel 7 \times h = 132$

$:\longmapsto \rm h = \cancel \frac{132}{22}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf h= 6 \: m} }}}$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{\text Height \: of \: Piller =6\: m}}}}}$