geometry
posted by bianca .
Find the height of a cone with a volume of 138 cubic meters and a base area of 46 square meters

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