Question

18. The volume of a solid figure varies with the square
of its radius when its height is constant and with its
height when its radius is constant. The solid figure
has a radius of 18 units, a height of 7 units and a
volume of 1152 cubic units. Instead, if its radius is
9 units and height is 21 units, what would be the
volume of the figure?

Answer 1

Answer:

Let the radius of the cylinder is r.

Height of cylinder = 2 units

Volume = πr

2

h=2πr

2

[∵h=2]

⟹2π(r+6)

2

=2πr

2

+y

⟹2πr

2

+24πr+72π=2πr

2

+y

∴y=24π(r+3)

⟹8πr

2

=2πr

2

+y

∴y=6πr

2

⟹6πr

2

=24π(r+3)⟹r

2

−4r−12=0

∴r=6units