Question

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.)

Answer 1

@ganeshie8

Answer 2

@Hero

Answer 3

@dan815

Answer 4

@pooja195

Answer 5

@triciaal

Answer 6

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

Answer 7

is this calculus?

Answer 8

yes

Answer 9

did you draw a picture of what is going on ?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

ok, now the derivative wrt x

Answer 14

what do u mean

Answer 15

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

Answer 16

and i got 3.4978761

Answer 17

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
\[ 12x^2 -240x + 500=0\\
3x^2 -60x+125=0
\]

Answer 18

and now do i find the maximum of that?

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

and then my answer from that is the final answer?

Answer 23

i got this

Answer 24

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

Answer 25

you should get a real number

Answer 26

i dont know how to simplify sqrt

Answer 27

im really bad at it

Answer 28

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

Answer 29

i got 2100 sorry

Answer 30

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

Answer 31

i am using a caluclator

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

@phi

Answer 36

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.

Answer 37

i got 2.362373842

Answer 38

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

Answer 39

so 2.36 is the final answer

Answer 40

yes