Question

The width of a plastic storage box is 1ft longer than the height. The length is 4 ft longer than the height. The volume is 36 ft³ . What are the dimensions of the box?

c. What equation represents the volume of the plastic storage box?

Answer 1

The volume of the plastic storage box is represented by the equation 36=(h+4)⋅(h+1)⋅h. Solving this cubic equation will provide the height, and the width and length can be found by adding 1ft and 4ft to the height respectively.

To find the dimensions of the plastic storage box when the volume is 36 ft³, we can set up the following equation based on the information provided:

w=h+1 (width is 1ft longer than the height)
l=h+4 (length is 4 ft longer than the height)

Thus, the equation representing the volume of the box is 36=(h+4)⋅(h+1)⋅h. Now, to solve for the height (h), we can expand and rearrange this into a cubic equation and solve for h using methods for solving cubic equations, such as factoring, graphing, or using the cubic formula. Once we find the height, we can then find the width and length by adding 1 and 4, respectively.

Answer 2

Answer:V = LWH volume = length x width x height240 = (2+H)((6+H)H = (H^2 + 8H + 12)H = H^3 + 8H^2 + 12HH^3 + 8H^2 + 12H - 240 = 0while there's no easy way to solve cubics, try some simple integers. You need an even integer2 doesn't work, too small, try 44^3 + 8(4)^2 + 12(4) -240 =0 Height = 4 feetdimensions are 4 x 10 x 6 feet = 240 ft/63divide h-4 into the cubic to get H^2 + 12H + 60the discriminate = 144-4(60) < 0 so there are no other real solutions4 feet by 6 feet by 10 feet is the only solution

Explanation: