<span>The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h:
x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x]
Simplify and get V = 250x-x^3/4
The volume will be a maximum when its first derivative is 0.
V' = 250-3/4x^2
Set to 0 and solve. x=18.26
Now plug into the volume function to find the maximum volume:
V=250(18.26)-(18.26)^3/4
V= 4564.35 - 1522.10 =3042.25</span>
Answer:
19
Step-by-step explanation:
Let me restate the given:
Diameter = 4 inches
height = 9 inches
The volume of a cone is formulated as V = (πr²h)/ 3
Since the formula uses a radius and the given is the diameter of a circle, then simply divide the diameter by 2 to get the radius.
r = 2 inches
Solve for volume of cone:
V = [ (3.14) (2)² (9) ] / 3
V = 37.7 in³
The answer is 37.70 in^3.
Answer:
Volume = (1/2)
[(1/2)x^3]
Step-by-step explanation:
The volume of a right rectangular prism is given by:
Volume = (length)*(width)*(height)
Volume = (x)*(x)*((1/2)x)
Volume = (1/2)
