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, 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:

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

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