Math, asked by shivangigautam4367, 10 months ago

The ratio between the radius of the base and the height of a cylinder is 2 : 3. Find the total surface area of the cylinder, it its volume is 1617 cm³.

Answers

Answered by sanjeevk28012

Answer:

Total surface area of cylinder is 769.3 sq cm .

Step-by-step explanation:

Given as :

For a cylinder

The ratio of radius of base and height of cylinder = 2 : 3

The volume of cylinder = V = 1617 cm³

Let The total surface area of cylinder = A sq cm

According to question

∵ Total surface area of cylinder = 2π r h + 2 π r² ......1

where r is radius , h is height of cylinder

Let The radius of base = 2 x

And The height of cylinder = 3 x

So , volume of cylinder = π r² h

Or, 1617 cm³ = π × ( 2 x)² × 3 x

Or, x³ = $\dfrac{1617}{37.68}$

Or, x³ = 42.91

i.e x = ∛42.91

∴ x = 3.50 cm

So, The radius of base = 2 × 3.50 = 7 cm

And The height of cylinder = 3 × 5.07 = 10.5 cm

Now, putting the value of r and h into eq 1

Total surface area of cylinder = 2π × 7 × 10.5 + 2 π 7²

Or, A = 2π × ( 73.5 + 49 )

Or, Area = 769.3 sq cm

So, Total surface area of cylinder = A = 769.3 sq cm

Hence, Total surface area of cylinder is 769.3 sq cm . Answer

Answered by nikitasingh79

Given : The ratio between the radius of the base and the height of a cylinder is 2 : 3 and volume is 1617 cm³.

Let , radius (r) of the cylinder be 2x and height (h) of the cylinder be 3x .

We know that, Volume of cylinder ,V = πr²h

1617= 22/7 (2x)² × 3x

[V = 1617 cm³]

1617 = 22/7 × 4x² × 3x

1617 = 22/7 × 12x³

1617 × 7 = 22 × 12x³

x³ = (1617 × 7)/(22 × 12)

x³ = (539 × 7)/(22 × 4)

x³ = (49 × 7)/(2 × 4)

x³ = 343/8

x = ³√343/8

x = 7/2

x = 3.5 cm

Now, radius of the cylinder , r = 2 x 3.5 = 7 cm and Height of the cylinder , h = 3x = 3 x 3.5 = 10.5 cm

Then, Total surface area of cylinder = 2πr(h + r)

= 2 x 22/7 x 7(10.5 + 7)

= 44 × 17.5

Total surface area of cylinder = 770 cm²

Hence the total surface area of cylinder is 770 cm².

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