A Hemispherical Bowl Of Internal And External Radii 3 Cm And 5 Cm Is Melted And Formed Into Right Circular Cylinder Of Radius 14 Cm .Find The Height O

A hemispherical bowl of internal and external radii 3 cm and 5 cm is melted and formed into right circular cylinder of radius 14 cm .find the height of the cylinder

 

Answer:

h = 1/3 cm

Step-by-step explanation:

A hemispherical bowl of internal and external radii 3 cm and 5 cm is melted and formed into right circular cylinder of radius 14 cm .find the height of the cylinder

First, calculate the volume of the hemispherical bowl:

V = (2/3) × π × r³

using internal radii (r = 3 cm) : V = (2/3) × π × (3 cm)³  = 18π cm³

using external radii (r = 5 cm) : V = (2/3) × π × (5 cm)³  = (250/3)π cm³

Subtract the volume of external and internal to get the volume of the bowl:

Volume of the bowl = external volume - internal volume

Volume of the bowl = (250/3)π cm³ - 18π cm³ = (196/3)π cm³

Since it is melted and formed to right circular cylinder, then the volume must be constant:

Volume of right circular cylinder = (196/3)π cm³ = π × r² × h

(196/3)π cm³ = π × (14 cm)² × h

solve for h

h = 1/3 cm