You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. Which of the

following dimensions will give you the greatest volume?
A. 12 in. by 22 in. by 4 in.
B. 10 in. by 20 in. by 5 in.
C. 14 in. by 24 in. by 2 in.
D. 10 in. by 24 in. by 6 in.

Suppose the squares you cut have side length x, [ then we have:
Length of box base: 20 - 2x
Width of box base: 30 - 2x
Height of box: x
Volume of box:
V = x(20 - 2x)(30 - 2x)
V = x(600 - 40x - 60x + 4x^2)
V = x(600 - 100x + 4x^2)
V = 600x - 100x^2 + 4x^3
dV/dx = 600 - 200x + 12x^2
Set that to zero:
12x^2 - 200x + 600 = 0
x = (-(-200) +/- sqrt((-200)^2 - 4(12)(600))) / (2*12)
x = (200 +/-

sqrt(40000 - 28800)) / 24
x = (200 +/- sqrt(11200)) / 24
x = (200 +/- sqrt(11200)) / 24
x =~ 12.74 or 3.92
Since you want whole numbers, x = 13 or 4
If x = 13, V = -312, but a negative number doesn't make sense, so we'll ignore that
If x = 4, V = 1056, so that's the maximum volume
The dimensions are:
Length of box base: 12
Width of box base: 22
Height of box: 4
By the way, this is calculus, not grade 8 math! ]

Expert answered|thederby|Points 1216|

Expert answered|thederby|Points 1216|

Question

Asked 5/28/2012 3:40:18 PM

0 Answers/Comments

Rating

There are no new answers.

area of a sphere **Weegy:** The formula for the area of a sphere is: 4 * pi * radius * radius. (More)

Question

Expert Answered

Asked 5/28/2012 2:50:25 PM

0 Answers/Comments

A conical tent made of canvas has a base that is 20 feet across and a slant height of 14 feet. To the nearest whole unit, what is the area of the canvas, including the floor? Use 3.14 for p **Weegy:** Floor is a circle of diameter 20, so radius is 10. [ Area = pi x radius squared = 3.14 x 100 = 314.
Surface area of the side is pi x radius x slant height = 3.14 x 10 x 14 = 439.6.
So total surface area is 314 + 439.6 = 753.6 square feet = 754 square feet to the nearest square foot as required. ] **User:** formula for finding the area of a sphere to the nearest square unit **Weegy:** The volume of a sphere can be found by the formula:
volume = 4/3 p r3
**User:** area of a sphere **Weegy:** The surface area of a sphere is given by the following formula:
\!A = 4\pi r^2.
(More)

Question

Expert Answered

Asked 5/28/2012 2:35:49 PM

0 Answers/Comments

volume for cylinder User: You are designing a new container for powdered laundry detergent. You are considering a cylindrical container with a diameter of 14 inches and a height of 18 inches. Find the volume of this container to the nearest cubic unit. Use a calculator. **Weegy:** Volume of cylinder = pi*h*r^2.. pi*18*7^2 = pi*882 cubic inches = 2771 cubic inches. **User:** Find the volume of a can of soup that has a height of 16 cm and a radius of 5 cm. Use 3.14 for p **Weegy:** Yes, you first find the area of the circular top or bottom and then multiply it by the height of the cylinder. The formula is V=h(pi*r^2) (More)

Question

Expert Answered

Asked 5/28/2012 3:00:17 PM

0 Answers/Comments

26,191,106 questions answered

There are no comments.