Question

A Rectangular box with square base and open at the top is to have a capacity of 16,823 cu.cm. Find the height of the box that requires minimum amount of the material required.

a. 14.12cm

b. 16.14cm

c. 12.13cm

d. 10.36cm

Answer 1

Perhaps the hardest part is coming up with the equations.

Answer 2

let the side of base =x and height=h

hx^2 = 16,823 so x = √(16823/h)

surface area of our bos = S(x)= x^2 +4xh

to find the minimum we calculate the first derivative
S'(x) = 2x + 4h
this is minimum for S'(x) =0
2x + 4h = 0 replace x by its value..

2√(16823/h) + 4h = 0
4h = -2√(16823/h) square both sides

16h^2 = 4(16823/h) cross multiply

h^3 = 4(16823)/16

so h = [(16823)/16]^(1/3) = 16.14cm

Answer 3

sorry the last line.. h = [(16823)/4]^(1/3) = 16.14cm

Answer 4

excellent, @hoblos

Answer 5

thanks :D

Answer 6

i reading hoblos answer i learn 1 or 2 w8.. im not finish =)

Answer 7

amazing like a prof

Answer 8

XD hope you understood that..

Answer 9

Find the height of the box that requires minimum amount of the material required.

That means find the least surface area (assumes all the sides and bottom are the same thickness).

So you need the equation for the surface area (without the top). 4 sides and 1 bottom
Then you need to replace the variable h (height) using the equation volume= h*x*x

See hoblos for the details.