-
Looking for HSC notes and resources? Check out our Notes & Resources page
Where am I going wrong (1 Viewer)
- Thread starter yashbb
- Start date
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.
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.