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Answer 1

Given that CSA of cylinder = 4110 m²

Volume = 3080 m³


We know that,

CSA = 2πrh

=> 2πrh = 4110

=> h = 4110/2πr

=> h = 2055/πr

And, volume = πr²h

=> πr²h = 3080

=> h = 3080/πr²

Equating the two, we get

$\frac{2055}{\pi r} = \frac{3080}{\pi {r}^{2} }$

Cancel π and r from both sides, thus we are left with,

${2055} = \frac{3080}{r} \\ \\ = > r = \frac{3080}{2055} \\ \\ = > r = 1.49 \: (approx)$

So, height = 2055/πr

Taking π as 22/7,
$2055 \div ( \frac{22}{7} \times \frac{3080}{2055} ) \\ \\ = > 2055 \div (22 \times \frac{440}{2055} ) \\ \\ = > 2055 \div \frac{9680}{2055} \\ \\ = > 2055 \times \frac{2055}{9680} \\ \\ = 436.26(approx)$

Hence, height = 436.26 m (approx)

Answer 2

Curved surface area (CSA) of the cylindrical pillar=4110 m²

So, 2πrh=4110

So, h=4110/2πr (writing 2πr in terms of height)

Now, it is given that the volume of the cylinder is 3080 m³ and that we have to find the length/height of the cylinder.

ATQ:-

πr²h=3080

Now put the value of h=4110/2πr in this equation.

22/7×r²×4110/2×22/7×r=3080

2055/22/7×22/7r=3080

14385/22×22/7r=3080

2055r=3080

r=3080/2055

r=616/411 (after cutting/cancelling the fraction)

Now, we have 'r' =616/411 m

So, height /length of the cylinder=4110/2×22/7×r

=4110/2×22/7×616/411

=2055/22×88/411

=2055/1936/411

=844605/1936

=436.262

=436.26 m (after rounding off)

So, the height/length of the cylinder=436.26 m