Question

The volume of a sphere is equal to the .......... of the volume of a cylinder whose height and diameter are equal to the diameter of sphere.

• A. two-third
• B. one-third
• C. one-fifth
• D. None of these

Answer 1

The correct option is A

two-third

Step 1: Given data

Since the height and diameter of the cylinder is equal to the diameter of the sphere

Radius of sphere$=r$

Radius of cylinder $=r$

Height of cylinder$=2r$

Step 2: Calculating the relation between the volume of the sphere and the volume of a cylinder

Volume of sphere$=\frac{4}{3}{\mathrm{\pi r}}^3$

Volume of cylinder$={\mathrm{\pi r}}^2\mathrm{h}$

As per the given data,

Volume of cylinder$=\mathrm{\pi }\times {\mathrm{r}}^2\times \left(2\mathrm{r}\right)=2{\mathrm{\pi r}}^3$

Volume of sphere$=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\left(2{\mathrm{\pi r}}^3\right)$

From the above, we can conclude that,

The volume of the sphere$=\frac{2}{3}\times$Volume of cylinder

Hence, option A is correct.