SOLUTION: THE HEIGHT OF A CONE IS HALF THE DIAMETER OF IT'S BASE.IF THE CONE'S HEIGHT IS 4 INCHES,WHAT IS THE CONE'S VOLUME TO THE NEAREST CUBIC INCHES?

Algebra ->  Volume -> SOLUTION: THE HEIGHT OF A CONE IS HALF THE DIAMETER OF IT'S BASE.IF THE CONE'S HEIGHT IS 4 INCHES,WHAT IS THE CONE'S VOLUME TO THE NEAREST CUBIC INCHES?      Log On


   

Question 960432: THE HEIGHT OF A CONE IS HALF THE DIAMETER OF IT'S BASE.IF THE CONE'S HEIGHT IS 4 INCHES,WHAT IS THE CONE'S VOLUME TO THE NEAREST CUBIC INCHES?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
h, height of cone
d, diameter of base
v, volume of cone
h=%281%2F2%29d
r=%281%2F2%29d=d%2F2
-
highlight_green%28v=%281%2F3%29h%2Ar%5E2%29

v=%281%2F3%29pi%28d%2F2%29%2Ar%5E2
v=%281%2F3%29%28d%2F2%29pi%28d%2F2%29%5E2
v=%281%2F3%29%281%2F4%29pi%2Ad%5E3

Recall h=d/2
d=2h
v simplifies through substituting for d,
v=%281%2F12%29pi%2A%282h%29%5E3
v=%288%2F12%29pi%2Ah%5E3
highlight%28v=%282%2F3%29pi%2Ah%5E3%29

Given was that h=4.
v=%282%2F3%29pi%2A64
highlight%28v=%28128%2F3%29pi%29

Exact steps can vary. Understand that rendering might make pi seem written as an exponent in some steps, but it is NOT an exponent; it is a factor.