Question

The number of litres of water $g$ in a circular tank varies jointly with the square of the radius $r^2$, and the depth $d$. If $g=30-16$ when $r=4$ and $d=2$, find the number of litres in the tank when $r=3$ and $d=1.5$

Answer 1

It is given that the number of litres of water $g$ in a circular tank varies jointly with the square of radius $r$ and the depth $d$ and$g=3016$ when $r=4$ and $d=2$, therefore,

$g=k{r}^{2}d\Rightarrow 3016=k{\times \left(4\right)}^2\times 2\Rightarrow 3016=k\times 16\times 2\Rightarrow 3016=32k\Rightarrow k=\frac{3016}{32}=\frac{377}{4}$

Thus, the general equation is $g=\frac{377}{4}{r}^{2}d$.

Since $r=3$ and $d=1.5$, therefore,

$g=\frac{377}{4}{\times \left(3\right)}^2\times 1.5=\frac{377}{4}\times 9\times 1.5=\frac{5089.5}{4}=1272.375$

Hence, $1272.375$ litres was there in the tank when radius is $3$ and depth is $1.5$.