Top-open tank

The top-open tank has the shape of a truncated rotating cone, which stands on a smaller base. The tank's volume is 465 m³, and the radii of the bases are 4 m and 3 m. Find the depth of the tank.

Correct answer:

h =  12 m

Step-by-step explanation:

$$\begin{gathered} r_1=4\text{m} \\ {r}_2=3\text{m} \\ V=465{\text{m}}^3 \\ V=\frac{1}{3}\pi h(r_1^2+r_1{r}_2+r_2^2) \\ h=\frac{3\cdot V}{\pi \cdot (r_1^2+r_1\cdot r_2+r_2^2)}=\frac{3\cdot 465}{3.1416\cdot (4^2+4\cdot 3+3^2)}=12\text{m} \end{gathered}$$

Try another example