The volume of a sphere with radius r is 4 / 3 pi r^3. Write a Python program to find the volume of spheres with radius 7 cm, 12 cm, 16 cm, respectively.

Why is the excluded volume $v$ four times the actual volume of molecules?

A conical-shaped container, whose radius of base is $r$ cm and height is $h$ cm, is full of water. A sphere of radius $R$ is completely immersed in the container in such a way that the surface of the sphere touches the base of the cone and its surfaces. The portion of water which comes out of the cone is:

A) $\frac{R^{2}}{r^{2} h}$
B) $\frac{r^{2}}{R^{2} h}$
C) $\frac{4 R^{3}}{r^{2} h}$
D) $\frac{4 r^{2}}{R^{2} h}$

A solid sphere of density $\rho$ and radius $R$ is floating in a liquid of density $\sigma$ with half its volume submerged. When the sphere is pressed down slightly and released, it executes simple harmonic motion of time period T. If viscous effects are ignored, then:

• $\sigma = 2 \rho$
• $T = 2 \pi \sqrt{\frac{2R}{3g}}$

The radius of a sphere is 6.01 cm. Its volume to four significant figures is:

• A 909.7 cm³
• B 909 cm³
• C 916 cm³
• D 909.67 cm³.

A solid sphere of radius 6 cm is converted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm and its height is 72 cm, find the uniform thickness of the cylinder.

• Option 1) 0.46 cm
• Option 2) 0.54 cm
• Option 3) 0.62 cm
• Option 4) 0.77 cm
• Option 5) 0.82 cm