Step-by-step explanation:
the volume of a pyramid is
V = length × width × height / 3
since we have a square pyramid, length = width.
V = 8×8×20/3 = 1280/3 ft³
but we need to look only at the smaller pyramid, as the oil is already standing 4 ft deep. so, the actual height is only 16 ft.
that is a shrinking factor of 16/20 = 4/5.
as we are dealing with similar triangles, the sand factor applies to all other lengths.
so, the square side length at 4 ft high is then
8 × 4/5 = 32/5 = 6.4 ft
and Vsmall = 6.4×6.4×16/3 = 655.36/3 ft³
2 ft³ in 1 second fills 2/(655.36/3) = 2×3/655.36 = 6/655.36 of the whole volume and makes the pyramid even smaller.
the question is now, what is the factor so that
Vsmaller = 6.4×f×6.4×f×16×f/3 = 655.36/3 - 2 =
= 655.36/3 - 6/3 = 649.36/3
f³×6.4²×16 = 649.36
f³ = 649.36/(6.4²×16) = 649.36/655.36 = 0.990844727...
f = 0.996938881...
that means the new smaller height is
16×0.996938881... = 15.9510221...
so, the height is increasing by 0.048977899... ft in this one second.
something does not fit between the problem description and the answer options.
