A rectangular storage container with an open top is to have a volume of 10cm^3. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 5 dollars per square meter. Solve for l in terms of w, solve for h in terms of w, and express the cost as a function of w alone.

Question

campbell_st · Answer

ok... so the dimensions are 

V = length x width x height

and you know length = 2 x width    and you know the volume

then 

10 = 2w x w x h

so 

$$5 = w^2 \times h$$

now looking at surface areas.... 

base  = length x width or  $$Base = 2w \times w = 2w^2$$

front and back    A = 2( length x height) 

$$A = 2( 2w \times h)$$

left and right sides

A = width x height

$$A = w \times h$$

so the total surface area is 

$$SA = 2w^2 + 2wh + wh$$

use the volume equation at the top, make h the subject and then subsitute into the surface area equation. 

so the cost function is 

Cost = base * 10 + (left and right) *5 + (front + back)*5

or 

$$Cost = 2w^2 \times 10 + 2(2w \times h) \times 5 + 2(w \times h) \times 5$$

hope this helps

anonymous · Answer

Thanks!