Question
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
✓
Answer
Let the radius of the hemisphere be r units.
Volume of a hemisphere = Surface area of the hemisphere
$\Rightarrow\frac{2}{3}\pi\text{r}^3=3\pi\text{r}^2$
$\Rightarrow\frac{2}{3}\text{r}=3$
$\Rightarrow\text{r}=\frac{9}{2}$
$\Rightarrow\text{d}=9\text{units}$
Hence, diameter of the hemisphere is equal to 9 units.
Volume of a hemisphere = Surface area of the hemisphere
$\Rightarrow\frac{2}{3}\pi\text{r}^3=3\pi\text{r}^2$
$\Rightarrow\frac{2}{3}\text{r}=3$
$\Rightarrow\text{r}=\frac{9}{2}$
$\Rightarrow\text{d}=9\text{units}$
Hence, diameter of the hemisphere is equal to 9 units.
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