# Math

A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 420 in^3 when a = 3?

1. You are cutting out 3-inch squares at the four corners.
Make a diagram.

width of base ---- x inches
length of base --- 2x inches, (you said so)
height of box ---- 3 inches

(x-6)(2x-6)(3) = 420
(x-6)(2x-6) = 140
x^2 - 18x + 36 = 140
2x^2 - 18x - 104 = 0

x = (18 ± √1156)/4
= (18 ± 34)/4
= 13 inches or a negative

so the sheet must have been 13 inches by 26 inches

posted by Reiny

## Similar Questions

1. ### Pre Cal

find the surface area of a box of hieght h whose base dimensions are p and q, and that satisfies either one of the following conditions: a) the box is closed. b) the box has an open top. c) the box has an open top and a square
2. ### algebra

Open-top box. Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then
3. ### calculus

A box with a square base and an open top is to have a volume of 68in^3 . Neglect the thickness of the material used to make the box, and find the dimensions of the box that would minimize the amount of material used. The width and
4. ### algebra

have 50 sq ft of material to make an open top box with a square base. a) use formula for surface area to express the height h of the box in terms of x. b) find the dimensions of the box that will produce the maximum volume.
5. ### calculus

An open box is to be made. This box is to have a bottom and four sides, but no top. The box is to be made from paper that is 7" by 12". Maximize the volume and find the height.
6. ### Calculus

I actually have two questions: 4. An open box is to be made from a rectangular piece of material 3m by 2m by cutting a congruent square from each corner and folding up the sides. What are the dimensions of the box of the largest
7. ### math

The length of an open-top box is 4 cm longer than its width. The box was made from a 480-cm^2 rectangular sheet of material with 6cm by 6cm squares cut from each corner. The height of the box is 6cm. Find the dimensions of the
8. ### Pre Cal 12

A 12cm by 8cm rectangular piece of metal is to be made into an open-top box by cutting a sqaure from corner and folding up the resulting flaps (sides). If the volume of the lidless box is 36 cm what are the integer dimensions of
9. ### Calculus

An open top box is made by cutting congruent squares from the corners of a 12 inch by 9 inch sheet of cardboard and then folding the sides up to create the box. What are the dimensions of the box which contains the largest volume?
10. ### Pre-calc

A cardboard box with an open top and a square bottom is to have a volume of 45 ft3 . Use a table utility to determine the dimensions of the box to the nearest 0.1 foot that will minimize the amount of cardboard used to construct

More Similar Questions