Question

if there is an error 0.01cm in the measurment of the radius 10cm of cylinder of fixed height 20cm then error in volume(cubic cm)_____​

Answer 1

$Given \: radius \: of \: a \: cylinder (r) = 10\:cm$

$Height (h) = 20 \:cm$

$Error \:in \: measurement \: of \: radius (\triangle r) = 0.01 \:cm$

$Volume \: of \:the \: Cylinder (V) = \pi r^{2} h$

$We \: need \: to \: find \: error \: in \\calculating \: the \: volume \: i.e \: \triangle V$

$\triangle V = \pi \frac{d(r^{2})}{dr} \times h\times \triangle r$

$= \pi \times 2r \times 20 \times 0.01 \\= \pi \times 2 \times 10 \times 20 \times 0.01 \\= 4\pi\: cm^{3}$

$\red{ Hence, Error \: in \: volume}\green { = 4\pi\: cm^{3} }$

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Answer 2

Step-by-step explanation:

the answer for this question is 4*π*cm²