Posted by **bianca** on Monday, April 9, 2012 at 9:19pm.

Find the height of a cone with a volume of 138 cubic meters and a base area of 46 square meters

- geometry -
**Anonymous**, Tuesday, April 10, 2012 at 8:14am
V = A * h

h = V / A = 138 / 46 = 3 m

- geometry -
**Bosnian**, Tuesday, April 10, 2012 at 10:11am
Volume of a cone:

V = ( 1 / 3 ) * r ^ 2 * pi * h

r ^ 2 * pi = B

The area of the circle base

V = ( 1 / 3 ) * B * h

V = 138 m ^ 3

B = 46 m ^ 2

138 = ( 1 / 3 ) * 46 * h Multiply both sides by 3

3 * 138 = 1 * 46 * h

414 = 46 h Divide both sides by 46

414 / 46 = h

h = 414 / 46

-------------------------

Remark:

414 = 2 * 3 * 3 * 23

46 = 2 * 23

-------------------------

h = 2 * 3 * 3 * 23 / ( 2 * 23 )

h = 3 * 3

h = 9 m

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