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Maths-

General

Easy

Question

If the ratio of base radius and height of a cone is $1 blank colon 2$ and percentage error in radius is $lambda blank percent sign comma$ then the error in its volume is

$λ %$
$2 λ %$
$3 λ %$
None of these

The correct answer is: $3 blank lambda percent sign$

Let $r$ be the base radius and $h$ be the height of the cone. Then, $2 r equals h.$ Let $V$ be the volume of the cone. Then,
$V equals fraction numerator 1 over denominator 3 end fraction pi r to the power of 2 end exponent h equals fraction numerator 4 pi blank r to the power of 3 end exponent over denominator 3 end fraction$

$rightwards double arrow fraction numerator d V over denominator d r end fraction equals 4 pi r to the power of 2 end exponent$

$therefore increment V equals fraction numerator d V over denominator d r end fraction increment r$

$rightwards double arrow increment V equals 4 pi r to the power of 2 end exponent blank increment r$

$rightwards double arrow fraction numerator increment V over denominator V end fraction cross times 100 equals fraction numerator 4 pi r to the power of 2 end exponent blank increment r over denominator fraction numerator 4 over denominator 3 end fraction pi blank r to the power of 3 end exponent end fraction cross times 100 equals 3 open parentheses fraction numerator increment r over denominator r end fraction cross times 100 close parentheses equals 3 lambda$

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