Where am I going wrong (1 Viewer)

[yashbb]

Q 27

 

[jimmysmith560]

Would this help?

Part (c):

Let's call the width x, and so this means the length is 3x.

V = length*width*height
= 3hx^2 = 4374

Rearrange to make h the subject:
h = 1458 / (x^2)

Now, we have found h depending on x.

The amount of steel needed is simply done by drawing a diagram and adding up all the lengths (remember not surface area, but the frame).

S = 4(length+width+height)
= 4(3x+x+h)
= 16x + 4h

(substitute the expression for h)

= 16x + 5832 / (x^2)

We need to differentiate S with respect to x, and solve dS/dx=0 to find the value for x such that S is at a minimum.

16 + (-2)5832 / (x^3) = 0
16x^3 = 11664
x = 9

h=18

Therefore, the width is 9, the length is 27 and height is 18.

 

[CM_Tutor]

Also need a test to prove that the result calculated does correspond to a minimum.