Question

Simple Question !!!


The volume of a cylinder is 1617 cm³. It's based and height are in the ratio 2:3 .Find the Curved Surface area of cylinder. ​

Answer 1

Answer:

770 cm^2.

Step-by-step explanation:

Given ratio = 2:3 and volume = 1617 cm^3.

Let the radius and height of the cylinder be 2x and 3x.   ---- (1)

Given volume of cylinder = 1617 cm^3

              pir^2h = 1617 cm^3

              (22/7) * (2x)^2 * 3x = 1617

               22/7 * 4x^2 * 3x = 1617

               x = 7/2.

Substitute x = 7/x in (1), we get

radius = 2 * 7/2 = 7

height = 3 * 7/2 = 21/2.

T.S.A of the cylinder = 2pir(h+r)

                                  = 2 * 22/7 * 7 * (21/2 + 7)

                                 = 22 * 35

                                 = 770 cm^2.

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Answer 2

Answer:

$\huge \hookrightarrow \sf \red{question}$

The volume of a cylinder is 1617 cm³. It's based and height are in the ratio 2:3 .Find the Curved Surface area of cylinder.

$\huge \bf \dag \blue{answer}$

Let the radius be r

Let the height be h

So,

$\sf \: \frac{radius}{height} = \frac{2}{3} \\ \\ \implies \: r = \frac{2}{3} h \\ \\ \implies \: h = \frac{3}{2} r$

$\star \sf \: volume = {\pi r}^{2} h = {1617cm}^{3} \\ \\ = \frac{22}{7} \times {r}^{2} \times \frac{3}{2} r = 1617 \\ \\ \implies \: {r}^{3} = \frac{ { \cancel{1617}} \: \: ^{ { \cancel{147}} \: \: ^{49} } \times 7 \times \cancel2}{ { \cancel{22}} \: \: ^{ \cancel{11}} \times \cancel3} \\ \\ = 49 \times 7 = 343$

${r}^{3} = 343 \\ \\ \therefore \: r = 3 \sqrt{343} = 7 \\ \\ \star \: h = \frac{3}{2} \times 7 \\ \\ = 10.5cm$

$\star \sf \: curved \: surface \: area = \\ 2 \times \frac{22}{ \cancel7} \times 10.5 \times \cancel 7 \\ \\ = 2 \times 22 \times 10.5 \\ \\ = 44 \times 10.5 \\ \\ \green{ \boxed{ \red{ = {462cm}^{2}}}}$

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