Cylinder-shaped part

A truncated cone-shaped part with base radii of 4 cm and 22 cm is to be recast into a cylinder-shaped part of the same height as the original part. What base radius will the new part have?

Final Answer:

r =  14 cm

Step-by-step explanation:

$$\begin{gathered} r_1=4\text{cm} \\ {r}_2=22\text{cm} \\ {V}_1=\frac{1}{3}\cdot \pi \cdot h\cdot (r_1^2+r_1\cdot r_2+r_2^2) \\ {V}_2=\pi \cdot r^2\cdot h \\ {V}_1=V_2 \\ \frac{1}{3}\cdot \pi \cdot h\cdot (r_1^2+r_1\cdot r_2+r_2^2)=\pi \cdot r^2\cdot h \\ {r}^2=\frac{1}{3}\cdot (r_1^2+r_1\cdot r_2+r_2^2) \\ r=\sqrt{\frac{r_1^2+r_1\cdot r_2+r_2^2}{3}}=\sqrt{\frac{4^2+4\cdot 22+22^2}{3}}=14\text{cm} \end{gathered}$$

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