Question

The height and radius of a cylinder are equal and its CSA is 2772 cm. Find the circumference
of the base of the cylinder.
​

Answer 1

Given:-

• The height and radius of a cylinder are equal.

• Its Curved Surface Area = 2,772cm²

To Find:-

• Circumference of the base of the cylinder.

Formula Used:-

• ${\boxed{\bf{{CSA\:of\: Cylinder= 2\pi rh}}}}$

• ${\boxed{\bf{{Circumference\:of\: Circle= 2\pi r}}}}$

Solution:-

Using Formula,

$\sf :\implies\:CSA\:of\: Cylinder= 2\pi rh$

As given in the question, radius (r) = height (h)

$\tt :\implies\:2,772= 2\pi r\times r$

$\tt :\implies\:2,772= 2\times \dfrac{22}{7}\times r^2$

$\tt :\implies\:r^2= \dfrac{2,772\times 7}{2\times 22}$

$\tt :\implies\:r^2= \dfrac{126\times 7}{2}$

$\tt :\implies\:r^2= 63\times 7$

$\tt :\implies\:r^2= 441$

$\tt :\implies\:r= \sqrt{441}$

$\tt :\implies\:r= 21\:cm$

Now,

$\sf :\implies\: Circumference\:of\: base= 2\pi r$

$\sf :\implies\: Circumference\:of\: base= 2\times \dfrac{22}{7}\times 21$

$\sf :\implies\: Circumference\:of\: base= 2\times 22\times 3$

$\sf :\implies\: Circumference\:of\: base= 132\:cm$

Hence, The Circumference of the base is 132cm.

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Answer 2

Answer:

132 cm

Step-by-step explanation:

$\boxed{ \huge{\mathfrak{ \colorbox{gray}{Given :-}}}}$

$\bull \: \: \: height \: of \: cylinder \: = radius \: of \: cylinder = r$

$\bull \: \: \: curved \: surface \: area \: of \: cylinder \: = 2272 \: {cm}^{2}$

$\huge\mathfrak{ \color{red}\colorbox{blue}{To find \: :-}}$

$\underline{ \bull \: \: \: circumference \: of \: base \: of \: cylinder}$

$CSA \: of \: cylinder = 2\pi rh$

$2 \times \frac{22}{7} \times r \times r\: = 2772$

$\frac{ \not2}{7} \times {r}^{2} = \not126 \: ^{63}$

${r}^{2} = 63 \times7$

${r}^{2} = 441$

$r = \sqrt{441}$

$r = 21$

$Since \: height = radius = 21cm$

$circumference \: of \: base \: radius = 2\pi r$

$2 \times \frac{22}{ \not7} \times \frac{ \not21 \: ^{3} }{1} = 132 \: cm$

$\huge\boxed{ \mathfrak{ \colorbox{green}{ \color{yellow}hope \: you \: like \: it}}}$