a pool for swimming laps is designed to be seven times as long as it is wide. Length = 7x Width = x
If the areas of the sides and the bottom are 90m^2, what are the dimensions of the pool if the volume of water it can hold is to be maximised?

Question

a pool for swimming laps is designed to be seven times as long as it is wide. Length = 7x Width = x
If the areas of the sides and the bottom are 90m^2, what are the dimensions of the pool if the volume of water it can hold is to be maximised?

ikram002p · Answer

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ikram002p · Answer

then
area=7x^2+2xh+14xh=90
7x^2+(2x+14x)h=90
h=(90-7x^2)/16x

volume(x)=7x^2*(90-7x^2)/16x (maximize this function)

ikram002p · Answer

$v(x)=630x-49x^3\
v'(x)=630-147x^2\
0=630-147x^2\
x^2=(30/7)\
x=\pm \sqrt (30/7)$
you could make a test and know that the positive one is the max :)

i think its like this , hope dint make a typo or something :)

anonymous · Answer

Thank you. I tried before I checked answer and got the same after about 3 hours thought. I guess I am right. Thank you again