V(x)=3π x^2(x+3)
W(x)=π/9 x^2(x+9)
W(3)=12π
The volume of the cone when x is 3 feet is 12π≈ 37.7 cubic yards.
Practice makes perfect
We are asked to write an expression for the volume of a right circular cone with the following dimensions.
Dimension
Expression
Radius of the base
r=3x
Height
h=x+3 yards
We are asked to write two different expressions.
One when x is given in yards, and one when x is given in feet.
In both cases the volume needs to be given in cubic yards.
x is measured in yards
Let's use the volume formula for the cone.
V=π r^2h/3
Now we will substitute the expressions in this volume formula.
The volume of the cone when x is measured in yards is V(x)=3π x^2(x+3) cubic yards.
x is measured in feet
If x is measured in feet but we still need the volume in cubic yards, we need to use a unit conversion.
xfeet isx/3yards
To find the new expression for the volume, we need to substitute x with x3 in V(x).
V( x)=3π x^2( x+3)
⇓
V( x/3)=3π ( x/3)^2( x/3+3)
Let's simplify this expression.
