A box with a square base $of$ length $x$ and height $h$ has a volume $V=x^{2}h.$ Complete parts $a.$ through $e.$

$a.V_x=$

$V_h=$

$b.$ For a box with $h=1\mathrm{.}8m,$ use a linear approximation $to$ estimate the change $in$ volume $ifx$ increases from $x=0\mathrm{.}5mtox=0\mathrm{.}52m.$

The change $in$ volume $ifx$ increases from $x=0\mathrm{.}5mtox=0\mathrm{.}52mis$

$(Simplify$ your answer.$)$

$c.$ For a box with $x=0\mathrm{.}5m,$ use a linear approximation $to$ estimate the change $in$ volume $ifh$ decreases from $h=1\mathrm{.}5mtoh=1\mathrm{.}46m.$

The change $in$ volume $ifh$ decreases from $h=1\mathrm{.}5mtoh=1\mathrm{.}46mis$

$(Simplify$ your answer.$)$

$d.$ For a fixed height, does $a10\%$ change $inx$ always produce $(approximately)a10\%$ change $inV?$

$No$

Yes

$e.$ For a fixed base length, does $a10\%$ change $inh$ always produce $(approximately)a10\%$ change $inV?$

Yes

$No$