Hemispherical Bowl:


The hemispherical bowl has a radius of 6 cm. To find the volume of water in the bowl, we can use the formula for the volume of a hemisphere: V = (2/3)πr³.

Cylindrical Vessel:


The water from the hemispherical bowl is transferred into a cylindrical vessel. The base of the cylindrical vessel has a radius of 3 cm. We need to find the height to which the water rises in the cylindrical vessel.

Volume of Hemispherical Bowl:


Using the formula V = (2/3)πr³, we can calculate the volume of the hemispherical bowl. Substituting the radius, we get:
V = (2/3)π(6)³ = 288π cm³.

Volume of Cylindrical Vessel:


The volume of the cylindrical vessel can be calculated using the formula V = πr²h, where r is the radius and h is the height.

Equating the Volumes:


Since the water from the hemispherical bowl is transferred into the cylindrical vessel, the volumes of both should be equal. Therefore, we can equate the volumes and solve for the height of the cylindrical vessel.
288π = π(3)²h
288 = 9h
h = 32 cm.

Height of Water in Cylindrical Vessel:


The height to which the water rises in the cylindrical vessel is 32 cm.

Explanation:


By equating the volumes of the hemispherical bowl and the cylindrical vessel, we can find the height to which the water rises in the cylindrical vessel. The volume of the hemispherical bowl is calculated using the formula for a hemisphere, and the volume of the cylindrical vessel is calculated using the formula for a cylinder. By setting these volumes equal to each other, we can solve for the height of the cylindrical vessel. In this case, the height is found to be 32 cm.

Volume of hemisphere =volume of cylinder
2πr2=πr2h
2*π*6*6=π*3*3*h
2*36*π/9*π=h
2*4=h
8cm=h