A family is building a pool that must be a rectangular prism and hold 1400ft³ and-3200ft³ of water. It must also be between 6-10ft deep. The family is also building a pool for their dog that has dimensions 1/4 the size of the family pool. I need to know what the dimensions for each pool should be...I can't come up with the right dimensions/water volume that works for both pools.

Question

anonymous · Answer

must hold BETWEEN 1400 and 3200ft³ of water

nottim · Answer

is this calculus? OR advanced functions? Or functions?

nottim · Answer

helllooo

nottim · Answer

@i_hate_math_

anonymous · Answer

Geometry

anonymous · Answer

you have,$$1400\le lwh \le 3200$$ and, for the dog pool, with each dimension 1/4 of the pool above,$$(1/4)^3lwh$$

anonymous · Answer

I still don't get it =/  I'm so confused

anonymous · Answer

but, we have a restriction on the depth, h:$$6\le h \le 10$$  There isn't going to be a unique answer here.  But choosing l=10 w=14 and h=10 works.  The dog pool dimensions will be l=10/4, w=14/4 and h=10/4.  There are many other possibilities which fit your restrictions.

anonymous · Answer

Ok..what I'm not understanding though, is how the dog pool is 1/4 the size of the family pool. Because shouldn't the volume be 1/4 as well as the dimensions?

anonymous · Answer

the dimensions of the dog pool are 1/4 the size of the regular pool.  The volume would not be 1/4 of the regular pool.  It would by (1/4)^3=1/64 of the regular pool.