A container has a capacity of $840$ cm$^3$ and is initially filled completely with water. The vo

Question

A container has a capacity of $840$ cm$^3$ and is initially filled completely with water. The volume, $V$ cm$^3$, of water in the container is given by $V = h^2 + 2h$, where $h$ cm is the height of the water level in the container. Due to leakage at the bottom of the container, the height of the water level in the container decreases at a rate of $\frac{5t}{3}$ cm/s, where $t$ is the time in seconds. Find the initial height of the water level in the container.[2] Show that the height of the water level $h$ can be expressed as $h = -\frac{5t^2}{6} + 28$.[2] Find the rate of decrease of volume when $t = 3$.[5]

Accepted Answer

(a)28 m (c)rate of decrease = 215 cm$^3$/s

2025 CHHY PRELIMS P1 Q2

2025 CHHY PRELIMS P1 Q2