Here we have two swimming pools. A rectangular pool is #6#ft long and a depth 1/3 of its width. A circular pool is #2#ft deep and has a diameter twice the width of the rectangular pool. What is the ratio of their volumes?

1 Answer
Alan N.
Mar 10, 2017

The ratio of the volumes of the pools is #pi#. Explanation below.

Explanation:

The pools are both regular 3 dimensional objects. The 'rectangular' pool is a cuboid and the 'circular' pool is a cylinder.

The volume of a cuboid is: length x width x depth

The volume of a cylinder is: #pir^2h# Where r is the radius and h the height (or depth in this case)

Let #x# be the width of the recangular pool in feet

We are told the the depth of the this pool is a third of its width =#x/3# feet. We are also told that its length is 6 feet.

#:.# the volume of the rectangular pool, #(V_r) = 6 xx x xx x/3#

#V_r = 2x^2# cubic feet

For the circular pool, we are told that its diameter is twice the width of the other, which is therefore #2x -> r=x# feet. We are also told that this pool is 2 ft deep.

#:.# the volume of the circular pool, #(V_c) = pi x^2 * 2# cubic feet

#V_c = 2pix^2# cubic feet

Hence the ratio of the volumes #=V_c/V_r#

#= (2pix^2)/(2x^2)#

#=pi# [or #pi#:1]

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