how many 1/4 can go into a rectangular prism of a volume of 10

Answer 1

10 divided by 1/4= 10/(1/4) = 10(4) = 40

40 boxes of volume 1/4 each fit into a rectangular prism of volume = 10

More common problems associated with a fixed volume for a rectangular prism

include minimizing the surface area:

Volume of a rectangular prism = length x width x height

V= LWH = 10

As a cube, each side is the cube root of 10 = about 2.15

It has the minimum surface area, less than any other rectangular prism with volume = 10

As a rectangular prism with top and bottom as squares

V=LWH = HL^2 = 10

H = 10/L^2

Surface Area = S = 2L^2 + 4HL = 2L^2 +10/L

S'(L) = 4L -10/L^2 = 0

4L^3 = 10

L^3 = 10/4 = 2.5

L= cube root of 2.5 = about 1.36

H=10/L^2 = about 10/1.36 = 7.35

1.36 by 1.36 by 7.35 would minimize surface area for a fixed volume of 10