Problema Solution
a natural history museum is building a pyramidal glass structure for its tree snake exhibit. its research team has designed a pyramid with a square base and with a height that is 2 yards more than a side of its base. the volume of the pyramid must be 147 cubic yards. what are the dimensions?
Answer provided by our tutors
let
a = the length of the side of the base
h = 2 + a the height that is 2 yards more than a side of its base
V = 147 yd^3 the volume
V = (1/3)(a^2)h
plug V = 147 and h = 2 + a into the equation
(1/3)(a^2)(2 + a) = 147
by simplifying we get:
a^3 + 2 z^2 - 441 = 0
click here to see the step by step solution of the equation:
for a = 7 the equation a^3 + 2 z^2 - 441 = 0 is true
thus a = 7 is one root
(a^3 + 2 a^2 - 441):(a - 7) = a^2 + 9a + 63
the equation a^2 + 9a + 63=0 has negative discriminant : D = b^2 - 4ac = 9^2 - 4*1*63 = - 134<0 thus it has no real solution
we conclude that a = 7 yd
h = 2 + 7
h = 9 yd
the length of the side of the base is 7 yards while the height is 9 yards.