a cone is attached to a hemisphere of radius 4 cm. if the total height of the object is 10 cm, find its volume.

Question

i find it quite tricky could u help me?????

Answer 1

The formula for the volume of a sphere is:

 

Volume (Sphere) = (4/3)*(pi)*(radius)³

 

Since we have a hemisphere, or half a sphere, the volume of the hemisphere will be one-half as much:

 

Volume (hemisphere) = (1/2)*(4/3)*(pi)*(radius)³ = (2/3)*(pi)*(radius)³

 

You know the radius = 4 cm, so you can plug in that value to compute the volume of the hemisphere.

 

The volume of a cone is:

 

V (cone) = (1/3)*(pi)*(radius)²*(height)

 

The radius is the same as the radius of the hemisphere (4 cm).  So what's its height?  The sphere's height is 4 cm and the total height of the sphere and cone is 10 cm. so the cone's height must be 10 cm - 4 cm = 6 cm.  Plug that in to compute the volume of the cone.

 

The total volume of the hemisphere and cone is:

 

V (total) = V (hemisphere) + V (cone)