11.088. A sphere, a cylinder with a square axial section, and a cone are given. The cylinder and the cone have the same bases, and their heights are equal to the diameter of the sphere. How do the volumes of the cylinder, the sphere, and the cone relate?
Solution.

$$
S_{\mathrm{ocH}_{\mathrm{u}}}=S_{\mathrm{och}_{\mathrm{k}}} ; \quad H_{\mathrm{k}}=H_{\mathrm{u}}=2 R_{\mathrm{u}} ; \quad R_{\mathrm{k}}=R_{\mathrm{u}}=R_{\mathrm{w}} . \quad \text { Volume } \quad \text { of } \quad \text { the } \quad \text { sphere }
$$

$V_{\mathrm{wl}}=\frac{4}{3} \pi R_{\mathrm{w}}^{3}=\frac{4}{3} \pi R^{3}$. Volume of the cone $V_{\mathrm{k}}=\frac{1}{3} \pi R^{2} H=\frac{2}{3} \pi R^{3}$. Volume of the cylinder $V_{\text {cyl }}=\pi R^{2} H=2 \pi R^{3}$. From this, the ratio:

$$
V_{\text {cyl }}: V_{\mathrm{u}}: V_{\mathrm{k}}=6: 4: 2=3: 2: 1
$$

Answer: $3: 2: 1$.