Question

the radius and height of a cylinder are in ratio 11:7 . If the curved surface area of the cylinder is 121 square units, then find its height and radius​

Answer 1

$\blue{\large\underline{\sf{Given- }}}$

The radius and height of a cylinder are in ratio 11 : 7.

The curved surface area of the cylinder is 121 square units

$\purple{\large\underline{\sf{To\:Find - }}}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Height \: of \: cylinder} \\ \\ &\sf{Radius \: of \: cylinder} \end{cases}\end{gathered}\end{gathered}$

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

Given that,

• The radius and height of a cylinder are in ratio 11 : 7.

• Curved Surface Area of cylinder = 121 square units.

So,

Let assume that

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Height \: of \: cylinder, h \: = \: 7x \: units} \\ \\ &\sf{Radius \: of \: cylinder, \: r \: = 11x \: units} \end{cases}\end{gathered}\end{gathered}$

We know,

Curved Surface Area of cylinder of radius r and height h is given by

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: CSA_{(Cylinder)} \: = \: 2 \: \pi \: r \: h \: \: }}}$

So, on substituting the values of CSA, height and radius, we get

$\rm :\longmapsto\:121 = 2 \times \dfrac{22}{7} \times 11x \times 7x$

$\rm :\longmapsto\:121 = 2 \times 22 \times 11 \times {x}^{2}$

$\rm :\longmapsto\:11 = 2 \times 22 \times {x}^{2}$

$\rm :\longmapsto\:1 = 2 \times 2 \times {x}^{2}$

$\rm :\longmapsto\: {x}^{2} = \dfrac{1}{4}$

$\rm\implies \:x = \dfrac{1}{2}$

Therefore,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Height \: of \: cylinder, h \: = \: \dfrac{7}{2} \: units} \\ \\ &\sf{Radius \: of \: cylinder, \: r \: = \dfrac{11}{2} \: units} \end{cases}\end{gathered}\end{gathered}$

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More information

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

Answer:

$\blue{\large\underline{\sf{Given- }}}$

The radius and height of a cylinder are in ratio 11 : 7.

The curved surface area of the cylinder is 121 square units

$\purple{\large\underline{\sf{To\:Find - }}}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Height \: of \: cylinder} \\ \\ &\sf{Radius \: of \: cylinder} \end{cases}\end{gathered}\end{gathered}$

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

Given that,

The radius and height of a cylinder are in ratio 11 : 7.

Curved Surface Area of cylinder = 121 square units.

So,

Let assume that

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Height \: of \: cylinder, h \: = \: 7x \: units} \\ \\ &\sf{Radius \: of \: cylinder, \: r \: = 11x \: units} \end{cases}\end{gathered}\end{gathered}$

We know,

Curved Surface Area of cylinder of radius r and height h is given by

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: CSA_{(Cylinder)} \: = \: 2 \: \pi \: r \: h \: \: }}}$

So, on substituting the values of CSA, height and radius, we get

$\rm :\longmapsto\:121 = 2 \times \dfrac{22}{7} \times 11x \times 7x$

$\rm :\longmapsto\:121 = 2 \times 22 \times 11 \times {x}^{2}$

$\rm :\longmapsto\:11 = 2 \times 22 \times {x}^{2}$

$\rm :\longmapsto\:1 = 2 \times 2 \times {x}^{2}$

$\rm :\longmapsto\: {x}^{2} = \dfrac{1}{4}$

$\rm\implies \:x = \dfrac{1}{2}$

Therefore,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Height \: of \: cylinder, h \: = \: \dfrac{7}{2} \: units} \\ \\ &\sf{Radius \: of \: cylinder, \: r \: = \dfrac{11}{2} \: units} \end{cases}\end{gathered}\end{gathered}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

More information

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