<ol class="i-list" start="2"><li><div class="list-item-paragraph">A manufacturer produces closed hollow cans. The top part is a hemisphere made of tin and the bottom part is a cylinder made of aluminium of cross-sectional radius $r$ cm and $h$ cm. There is no material between the cylinder and the hemisphere so that any fluid can move freely within the container. At the beginning of an experiment, a similar-shaped can of dimensions $r=4$and $h=10$, is filled to its capacity with water. Due to a hole at its base, water is leaking at a constant rate of 2 $\mathrm{c}{{\mathrm{m}}^{3}}{{\mathrm{s}}^{-1}}$ when the can is standing upright. Find the exact rate at which the height of the water is decreasing 80 seconds after the start of the experiment.<span class="inline-marks">[5]</span></div><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1770107633508-s35co2fu8s9.png" alt="List item image" class="alignleft custom-width" style="max-width: min(250px, 100%); height: auto;" /></div></li></ol>

A manufacturer produces closed hollow cans. The top part is a hemisphere made of tin and the bottom part is a cylinder made of aluminium of cross-sectional radius $r$ cm and $h$ cm. There is no material between the cylinder and the hemisphere so that any fluid can move freely within the container. At the beginning of an experiment, a similar-shaped can of dimensions $r=4$and $h=10$, is filled to its capacity with water. Due to a hole at its base, water is leaking at a constant rate of 2 $\mathrm{c}{{\mathrm{m}}^{3}}{{\mathrm{s}}^{-1}}$ when the can is standing upright. Find the exact rate at which the height of the water is decreasing 80 seconds after the start of the experiment.

Applications of Differentiation

H2 Math

International Baccalaureate Higher Level Mathematics

2018 MJC P1 Q9 [Modified]

2018 MJC P1 Q9 [Modified]

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