Question

a box has dimension of 10-x, 10-x and 1/2x. Write an expression in terms of x for the volume of the box.

b. use the expression to calculate the volume of x..

c. what is the maximum volume of the box?

Answer 1

The volume(V) of the box would be L*W*H where
L is the length 10-x
W is the width 10-x
H is the height 1/2 x
V=(x/2)(10-x)^2

Answer 2

I don't understand what "calculate the volume of x" means?

Answer 3

x must be the vollume of the box. How would you calculate the maximum volume?

Answer 4

I am not sure. I would assume that x should be small so that 10-x would be as big as possible but I am not really sure.

Answer 5

ok. so say ur assumption is correct. what would be the final result

Answer 6

do you think the height is (1/2)x or 1/(2x)? If it is the first, then the volume will go down as x gets smaller. in the second. the volume goes up as x gets smaller

Answer 7

i think its 1/(2x)

Answer 8

The maximum volume would be when x becomes infinitely small, that would make the volume infinitely big. hmm. you might need to find someone who gets this better than me.

Answer 9

If the volume of the rectangular solid container is V(x) = ((x/2)(10-x)^2), then the maximum volume of the box would occur at x = 10/3 yielding a maximum volume of V(10/3) = 2000/2.

http://www.wolframalpha.com/input/?i=y+%3D%28x%2F2%29%2810-x%29%5E2