Question

The curved surface area of a cylindrical pillar is 264 m^2 and its volume is 924 m^3. The height of the pillar is

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given-\begin{cases} &\sf{Volume_{(cylinder)} = 924 \: {m}^{3} } \\ &\sf{CSA_{(cylinder)} = 264 \: {m}^{2} } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: Find - \begin{cases} &\sf{height_{(cylinder)}}\end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used - }}}}  \end{gathered}$

$\underline{ \boxed{ \bf \: Volume_{(cylinder)} = \: \pi \: {r}^{2}h}}$

$\underline{ \boxed{ \bf \: CSA_{(cylinder)} = 2\pi \: rh}}$

where,

$\: \: \: \: \: \: \: \: \: \bull \: \sf \:r \: is \: radius \: of \: cylinder$

$\: \: \: \: \: \: \: \: \: \bull \: \sf \:h \: is \: height \: of \: cylinder$

$\large\underline{\sf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf \:Let-\begin{cases} &\sf{radius \: of \: cylinder \: = \: r \: meter} \\ &\sf{height \: of \: cylinder \: = \: h \: meter} \end{cases}\end{gathered}\end{gathered}$

Given that,

$\rm :\longmapsto\:Volume_{(cylinder)} = 924$

$\rm :\longmapsto\:\pi \: {r}^{2}h = 924 - - - (1)$

and

$\rm :\longmapsto\:CSA_{(cylinder)} = 264$

$\rm :\longmapsto\:2\pi \: rh = 264 - - - (2)$

Now, Divide equation (1) by equation (2), we get

$\rm :\longmapsto\:\dfrac{\pi \: {r}^{2}h}{2\pi \: rh} = \dfrac{924}{264}$

$\bf\implies \:r \: = \: 7 \: m$

On substituting the value of 'r' in equation (2), we get

$\rm :\longmapsto\:2 \times \dfrac{22}{7} \times 7 \times h = 264$

$\bf\implies \:h \: = \: 6 \: m$

$\overbrace{ \underline { \boxed { \bf \therefore \: The \: height_{(cylinder)} \: is \: 6 \: meter}}}$

Additional Information :-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length²+breadth²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

Answer 2

$\begin{gathered}\begin{gathered}\bf \: To \: Find - \begin{cases} &\sf{height_{(cylinder)}}\end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used - }}}} \end{gathered}$

$\underline{ \boxed{ \bf \: Volume_{(cylinder)} = \: \pi \: {r}^{2}h}}$

$\underline{ \boxed{ \bf \: CSA_{(cylinder)} = 2\pi \: rh}}$

where,

$\: \: \: \: \: \: \: \: \: \bull \: \sf \:r \: is \: radius \: of \: cylinder$

$\: \: \: \: \: \: \: \: \: \bull \: \sf \:h \: is \: height \: of \: cylinder$

$\large\underline{\sf{Solution-}}$

Solution−

$\begin{gathered}\begin{gathered}\begin{gathered}\bf \:Let-\begin{cases} &\sf{radius \: of \: cylinder \: = \: r \: meter} \\ &\sf{height \: of \: cylinder \: = \: h \: meter} \end{cases}\end{gathered}\end{gathered}\end{gathered}$

Given that,

$\rm :\longmapsto\:Volume_{(cylinder)} = 924$

$:\longmapsto\:\pi \: {r}^{2}h = 924 - - - (1)$

and

$\rm :\longmapsto\:CSA_{(cylinder)} = 264$

$\rm :\longmapsto\:2\pi \: rh = 264 - - - (2)$

Now, Divide equation (1) by equation (2), we get

$\rm :\longmapsto\:\dfrac{\pi \: {r}^{2}h}{2\pi \: rh} = \dfrac{924}{264}$

$\bf\implies \:r \: = \: 7 \: m$

On substituting the value of 'r' in equation (2), we get

$\rm :\longmapsto\:2 \times \dfrac{22}{7} \times 7 \times h = 264$

$\bf\implies \:h \: = \: 6 \: m$

$\overbrace{ \underline { \boxed { \bf \therefore \: The \: height_{(cylinder)} \: is \: 6 \: meter}}}$

$\large{\red{ \tt \: Additional \: \: \: Information :-}}$

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length²+breadth²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²