A solid body consists of a cylinder surmounted by a hemisphere of the same radius. The total length of the body, measured along the central axis of cylinder, is 10cm. If the radius of the hemisphere is xcm,show that the volume vcm^3, of the solid body is given by v=pi x^2/3(30-x).

Answer 1

plug and chug
h = 10 - x
v = pi x^2 h + (2/3) pi x^3
= pi x^2(10-x) + (2/3) pi x^3
= pi [ 10 x^2-x^3 + (2/3)x^3 ]
= (pi/3) [30 x^2 - x^3 ]
= (pi x^2/3)(30 -x)

Answer 2

h=10-x
v of object = v of cylinder v of hemisphere
then u are good to go

Answer 3

All the answers are not understandable Without diagram

Answer 4

H=10-x
V=πx^2(10-x)+2/3πx^3
V=π(x^2(10-x)+2/3x^3)
V=π(10x^2-x^3+2/3x^3)
V=π(10x^2-1/3x^3)
V=πx^2(10-1/3x)
V=πx^2/3(30-x)