A box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides.
What is the maximum volume this box could have? (Round your answer to two decimal places.)

- anonymous

- jamiebookeater

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- anonymous

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- anonymous

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## More answers

- anonymous

- anonymous

- anonymous

i already did it but i got it wrong 2 times please help

- phi

is this calculus?

- anonymous

yes

- phi

did you draw a picture of what is going on ?

- anonymous

u want me to show u what i have gotten so far?

- anonymous

yes i did i got the equation (50-2x)(10-2x)(x)

- anonymous

then all together 4x^3-120x^2+500x

- phi

ok, now the derivative wrt x

- anonymous

what do u mean

- anonymous

then i found the maximum of the graph of 4x^3-120x^2+500x

- anonymous

and i got 3.4978761

- phi

you have
\[ V = 4x^3-120x^2+500x \]
and people find the derivative of that
\[ \frac{dV}{dt} = 12x^2 -240x + 500 \]
and set = to zero
\[ 12x^2 -240x + 500=0\\
3x^2 -60x+125=0
\]

- anonymous

and now do i find the maximum of that?

- phi

you find what x's make the equation 0
use the quadratic formula

- anonymous

so now i use the quadratic formula or do i put it in the graphing calculator and find the maximum?

- phi

we don't want the maximum of the derivative, we want to find the x value that makes the derivative 0. so we solve for x in
3x^2-60x+125=0
using the quadratic formula

- anonymous

and then my answer from that is the final answer?

- anonymous

i got this

- anonymous

\[60+-\sqrt{-5100} all divided by 6

- phi

you should get a real number

- anonymous

i dont know how to simplify sqrt

- anonymous

im really bad at it

- phi

the number inside the square root should be -60*-60 - 4*3*125
that is not -5100

- anonymous

i got 2100 sorry

- phi

I would use a calculator and get a decimal answer. they say
(Round your answer to two decimal places.)

- anonymous

i am using a caluclator

- anonymous

i did 4(3)125 and got 1500
then -60*-60 is 3600 and those 2 subtracted is 2100 right???

- phi

yes so
\[ x = \frac{60\pm\sqrt{2100}}{6} \]

- anonymous

i got 60+10 sqrt{21}
all divided by 6 is that right

- anonymous

- phi

that root will give you 10+ (sqrt(21))/6 which is bigger than 10
one of your sides is length 10, so x has to be smaller than 10
I would use the other root.

- anonymous

i got 2.362373842

- phi

yes, that looks ok. round to 2 decimal places.

- anonymous

so 2.36 is the final answer

- phi

yes

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