Question

Can someone please help me with Calculus 1 Maximum Volume.
Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 337.5 square centimeters

Answer 1

whats the equation for the surface area of a rectangular solid with a square base?

Answer 2

if u draw it that might help

Answer 3

not sure

Answer 4

alright lets say the length and width of the base of the box equals x and the height equals y. Since the surface area is the area of all the faces added up then the surface area of this rectangle would b
2x^2 for the base and the top
4xy for the four faces going around
so
4xy and 2x^2=Surface area
and u know surface area equals 337.5 so
4xy+2x^2=337.5

Answer 5

how do you know length and width is the same?

Answer 6

because the base is a square

Answer 7

oh right thanx

Answer 8

now u kno that volume equals length*width*height so for our rectangle itll b
V=yx^2

Answer 9

to find the maximum volume u want to differentiate the volume equation but u cant because there r 3 variables. so u need to use ur Surface area equation solve for a variable and then replace that variable in ur volume equation

Answer 10

so solve for y in the surface area equation i gave u