Question

A sphere of radius r is inscribed in the cylinder such that the
curved surface of the sphere touches the cylinder. Find the
volume of the cylinder which is not occupied by the sphere.

Answer 1

Step-by-step explanation:

$\pi {r}^{2} {h - 4 \div 3r$

Answer 2

Volume of the cylinder which is not occupied by the sphere $\mathbf{\frac{2}{3}\pi R^{3}}$

Step-by-step explanation:

• Given data about sphere

        Radius of sphere = R

        $\mathbf{\textrm{Volume of sphere}(V_{s})=\frac{4}{3}\times \pi \times R^{3}}$      ...1)

• Given data about cylinder

        Radius of cylinder = R

        Height of cylinder (H) = 2R

        $\mathbf{\textrm{Volume of cylinder}(V_{c})=\pi \times R^{2}\times H}$

• On putting value of height in terms of radius

        $\mathbf{\textrm{Volume of cylinder}(V_{c})=\pi \times R^{2}\times 2\times R=2\pi R^{3}}$     ...2)

• Remaining volume of cylinder = $\mathbf{V_{c}-V_{s}}$

        Remaining volume of cylinder $\mathbf{=2\pi R^{3}-\frac{4}{3}\pi R^{3}}$

        Remaining volume of cylinder$\mathbf{=\frac{6\pi R^{3}-4\pi R^{3}}{3}}$

        Remaining volume of cylinder$\mathbf{=\frac{2}{3}\pi R^{3}}$