0
If you were to cut out the four corners of a 8.5 by 11inch piece of paper to make a box what would be the measurement of the squares you cut out to get the greatest volume?
Wiki User
∙ 14y ago
Ok.. let h be the height of the finished box, w be the width of the box, and l be the length of the box.
You will cut h x h squares out of the 8.5"x11" paper.
So..
w=8.5-2h
l=11-2h
The Volume of the box (V) = w*l*h = (8.5-2h)(11-2h)h
I won't go through the multiplication here, but V = 4h3 - 39h2 +93.5h
There are two ways to find the maximum, graphing the function and finding the zeros of the first derivative.
Since this is a classic first semester calculus problem, I will do the latter.
Using the power rule: dV/dx = 12h2-78h+93.h
Using the quadratic equation: h = (78+-sqrt(1596))/24
h ~= 1.585" or h ~= 4.915
V(1.585) ~= 66.1482
V(4.915) ~= -7.64823
Obviously, h ~= 1.585" is the local maximum.
Therefore, you would cut four 1.585"x1.585" squares to make your box.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
How tall is pleasure p?
5ft 11inch
How much is 11inch in centimeters?
By unit of length and distance and conversion ,we can say that 11 in =27.94 cm
5ft 11inch equals how many meters?
5 feet 11 inches=1.8034 meters
What weight do you have to be to stop using a booster seat?
in the UK it is based on height the boundary is 150cm or 4ft 11inch
What size softball do 9 and10 year olds need?
7-9 year olds use a 11inch ball 10-12 year olds use a 12inch ball
What size softball does 6 and under use?
If this is not T-ball then they should be using an 11inch softball. If it is a t-ball league then they should be using an RIF safety ball (t-ball) anywhere from level 1 to level 5. (level 1 is softest).
Anybody know where I can get a strong binder folder that'll be able to hold my 11inch MacBook Air Which is relatively light thank you?
A good place to find a strong binder that will hold an 11 inch Macbook Air would be a computer supply store, such as Staples or Best Buy. You might also try Amazon or Ebay.
Wider tires on smaller rims 13 inch tire on 11inch rims for farm tractor?
18.4 inch tractor tires are on 16 inch rims in most cases. I don't know what the limit would be I would think 13 inch on 11 inch rims would be fine. The hardest part would be to get it inflated if it is tubeless. There are tricks to that though.
What is the best baseball glove for 6 year old child?
The best glove for a 6 yr old would be anything soft and with a sizeable pocket. approx. 11inch glove with a pocket to hold a ball. Too many youth gloves are built for aesthetics and not for functionality. Glove manufactures make gloves for youth that are designed to catch. Try glove maker Akadema...best in the business
What is the ideal weight for a 16-year-old male that is 5ft 11inch tall with a medium frame?
Its hard to say b/c you are still growing at age 16 but for an adult of that size the ideal weight is 172lb. The way you calculate the desirable weight for a male is you take 106lb for the first 5ft and add 6lb for every additional inch. This of course does not take into account the percent of muscle and fat in the body.
How wide was Queen Victoria?
So Heavy her bed weighed a ton that's like the same weight as a car!She must have been well fed! Suffice it to say that it was not polite to report the exact dimensions of the portly queen so her exact size can only be estimated.If you are wondering about the ship named the Queen Victoria, there have been 2 notable ships by that name.The PS Queen Victoria was a paddle wheel steamer built in 1838 for the City of Dublin Steam Packet Company and which was shipwrecked in 1853 with the loss of over 80 passengers and crew.The exact dimensions of the ship are not readily available.MS Queen Victoria (QV) is a cruise ship in the Cunard Line fleet, named after Queen Victoria. It has a beam (width) of 106 ft (32.3 m) at the waterline, 120 ft (36.6 m) at the extreme (bridge wings).The TS Queen Mary originally sailed as TSQueen Victoria from 1933 to 1935. It had a beam of 35.1 ft (10.7 m).
