# Answer to Question #13855 in Geometry for peter

Question #13855

The volume of a cone is 360cm3. If the height of the cone is 30cm,find the length of the base

Expert's answer

Assume that the base is a circle of radius r, so the area of the base is

S

= pi * r^2

The height of the cone is h=30 cm.

Then the volume is

equal to

V = h * S / 3 = 360

pi * r^2 * h = 3

V

whence

r = square_root ( 3 V/(pi*h) )

Therefore

the length of the base is

L = 2 * pi * r =

= 2 * pi *

square_root ( 3 V/(pi*h) )

= 2 * square_root ( 3 V pi /h )

= 2 * square_root ( 3 * 360 * pi / 30 )

= 2 * square_root ( 36 pi )

= 12 * square_root ( pi )

= 21.2694 cm

S

= pi * r^2

The height of the cone is h=30 cm.

Then the volume is

equal to

V = h * S / 3 = 360

pi * r^2 * h = 3

V

whence

r = square_root ( 3 V/(pi*h) )

Therefore

the length of the base is

L = 2 * pi * r =

= 2 * pi *

square_root ( 3 V/(pi*h) )

= 2 * square_root ( 3 V pi /h )

= 2 * square_root ( 3 * 360 * pi / 30 )

= 2 * square_root ( 36 pi )

= 12 * square_root ( pi )

= 21.2694 cm

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