[It is given that the volume of a circular cone with base radius $r$ and height $h$ is \(\frac{1

Question

[It is given that the volume of a circular cone with base radius $r$ and height $h$ is $\frac{1}{3} \pi r^2 h$.] A container is made in the shape of an inverted open right circular cone. The height of the container is $6$ metres, and the radius is $2$ metres. The container is initially empty. Water is poured into the container while, at the same time, water is leaking from a hole at the bottom of the container at a rate of $0.03$ m${}^3$/s, resulting in the depth of water in the container to be increasing at a rate of $0.1$ m/s. At time $t$ seconds after the start, the depth of water in the container is $h$ metres. Find, in terms of $h$, an expression for the volume of water in the container at time $t$ seconds after the start.[2] Find the rate at which water is being poured into the container when the depth of water in the container is $3$ metres.[4]

Accepted Answer

(a)$V=\frac{1}{27}\pi h^2$ (b)0.344 m/s

2025 TMJC P1 Q6

2025 TMJC P1 Q6