The radius of a sphere, 'r', is equal to the radius of the base of a right circular cylinder. The total volume of these two solids = $$\frac{7}{3}$$​ $$\text{πr}^3$$​. If 'h' is the height of the cylinder, find $$\frac{\text{h}}{\text{r}}$$​.

Correct option is C

Given:

The radius of the sphere = radius of the base of the right circular cylinder = r

Total volume =$$\frac{7}{3} \pi r^3$$​​

Formula Used:

Volume of a sphere: $$V_{\text{sphere}} = \frac{4}{3} \pi r^3$$​​

Volume of a cylinder: V$$_{\text{cylinder}} = \pi r^2 h$$​​

Solution:

​$$\frac{4}{3} \pi r^3 + \pi r^2 h = \frac{7}{3} \pi r^3$$​​

​$$\pi r^2 h = \frac{7}{3} \pi r^3 - \frac{4}{3} \pi r^3$$​​

​$$\pi r^2 h = \frac{3}{3} \pi r^3$$​

​$$\pi r^2 h = \pi r^3$$​

​$$r^2 h = r^3$$​

h = r

​$$\frac hr =1$$​​