Question

there is a hemispherical bowl. A cone is to be made such that if it filled with water twice the bowl will just filled completely.State how will you decide the radius and perpendicular height of the cone

Answer 1

Answer:

To fulfill above condition radius of cone equals to radius of hemispherical bowl and height is 4 times the radius of hemisphere.

Step-by-step explanation:

Given that there is a hemispherical bowl. A cone is to be made such that if it filled with water twice the bowl will just filled completely. we have to decide the radius and height of cone so that the above condition fulfilled.

As, $\text{volume of cone=}\pi r^2\frac{h}{3}$

$\text{Volume of hemisphere=}\frac{2}{3}\pr R^3$

$\frac{\text{volume of cone}}{\text{volume of hemisphere}}=\frac{\pi r^2\frac{h}{3}}{\frac{2}{3}\pr R^3}=\frac{r^2h}{2R^3}$

which shows if the radius of cone equals to radius of hemispherical bowl and height is 4 times the radius of hemisphere then

$\frac{\text{volume of cone}}{\text{volume of hemisphere}}=2$

i.e Volume of cone=2(volume of hemispherical bowl)

To fulfill above condition radius of cone equals to radius of hemispherical bowl and height is 4 times the radius of hemisphere.