Explanation:

To find the ratio of the volume of the sphere to that of the cylinder, follow these steps:

- Let r be the common radius of the sphere and the base of the cylinder.

- The volumes of sphere \( V_{\text{sphere}} \) and cylinder \( V_{\text{cylinder}} \) are calculated as follows:

- Sphere Volume: \( V_{\text{sphere}} = \frac{4}{3} \pi r^3 \)

- Cylinder Volume: \( V_{\text{cylinder}} = \pi r^2 h \)

- Given the ratio of the radius and height of the cylinder is 3 : 4, if radius \( r \) then height \( h \) is \( \frac{4}{3}r \).

- This gives the cylinder's volume as \( \pi r^2 \left(\frac{4}{3}r\right) = \frac{4}{3} \pi r^3 \).

- Now, compare the volumes: \( \frac{V_{\text{sphere}}}{V_{\text{cylinder}}} = \frac{\frac{4}{3} \pi r^3}{\frac{4}{3} \pi r^3} = 1 \).

So, the ratio is 1 : 1, confirming that both volumes are equal.

- Option 3: 1 : 1 is indeed the correct answer.