Question
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?
✓
Answer
Let the radius of the solid hemisphere be r units. Numerical value of surface area of the solid hemisphere $=3\pi\text{r}^2$ Numerical value of volume of the solid hemisphere $=\frac{2}{3}\pi\text{r}^3$ It is given that volume and surface area of the solid hemisphere are numerically equal. $\therefore\frac{2}{3}\pi\text{r}^3=3\pi\text{r}^2$ $\Rightarrow2\text{r}=9\ \text{units}$ Thus, the diameter of the hemisphere is 9 units.
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