Question

The volume of a sphere is equal to two-third of the volume of the cylinder whose height and diameter are equal to the diameter of the sphere

• A. True
• B. False

Answer 1

The correct option is A True

Let the radius of the sphere be $\text{r}$

So diameter of sphere $=2\times \text{r=2r}$

According to the question

height and diameter of cylinder $=$diameter of sphere

So height of cylinder $=2\text{r}$

We know that volume of cylinder $=\mathrm{\pi }{\text{r}}^2{\text{h=πr}}^2{\text{(2r)=2πr}}^3$

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

Then according to the given condition

volume of sphere$=\frac{2}{3}$volume of cylinder

$$\begin{gathered} \frac{4}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\left(2{\mathrm{\pi r}}^3\right) \\ \frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}{\mathrm{\pi r}}^3 \end{gathered}$$

Hence the given condition is true .