GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

Question : 40 of 65

Marks: +1, -0

The diameter and height of a right circular cylinder are

3 {cm}

and

4 {cm}

, respectively. The absolute error in each of these two measurements is

0.2 {cm}

. The absolute error in the computed volume (in

{cm}^{3}

, round off to three decimal places), is_______________.

Solution:

diameter

= {d}=3 {cm}

height

= {h}=4 {cm}

{e}_{ {d}}= {e}_{ {h}}=± 0.2 {cm}

{v}= {f}( {d}, {h})

{v}=\;{π {d}^{2}}/{4} {h}

{d} {v}=(\;{∂ {v}}/{∂ {d}}) {d} {d}+(\;{∂ {v}}/{∂ {h}}) {dh}

=\;{π {dh}}/{2} × {e}_{ {d}}+\;{π {d}^{2}}/{4} × {e}_{ {h}}

∴

Absolute error

=5.18 {cm}^{3}

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