+1982 
Circular cones A and B are congruent. If the volume of cone B is 8π in3, then its height, h =
A) 4 in
B) 6 in
C) 8 in
D) 10 in
E) 12 in
+129852 Vcone = pi * radius^2 * height / 3 ....so we have
8 pi = pi * (x/2)^2 * (x + 2) / 3 divide out pi.....multiply both sides by 3
24 = x^2 ( x + 2)/4 multiply both sides by 4
96 = x^2 ( x + 2)
96 = x^3 + 2x^2
x^3 + 2x^2 - 96 = 0
The real solution to this is x = 4
So....the height of B = x + 2 = 6
+1982 Cone A and cone B are congruent, so they must have the same volume. Cone A has volume of 8pi in^3 (because we're told cone B has this volume)
focus on cone A only for now
r = radius = d/2 = x/2
h = height = x+2
V = volume of cone
V = 8pi
V = (1/3)*pi*r^2*h
8pi = (1/3)*pi*(x/2)^2*(x+2)
8pi = (1/3)*pi*((x^2)/4)*(x+2)
8pi = pi*((x^2)/12)*(x+2)
8 = ((x^2)/12)*(x+2) ... divided both sides by pi
12*8 = x^2(x+2) ... multiplied both sides by 12
96 = x^3+2x^2
0 = x^3+2x^2-96
Using a graphing calculator, I found the solution to that equation to be x = 4. Basically you are looking for the x intercept of f(x) = x^3+2x^2-96
So,
h = x+2
h = 4+2
h = 6
Answer: B) 6 in
