A square-based prism has volume 512 cm3 a) What are the possible whole-number dimensions of the prism? b) Which dimensions produce the prism with the least surface area?

Question

a) What are the possible whole-number dimensions of the prism?

b) Which dimensions produce the prism with the least surface area?

Answer 1

least surface are prisom is a cube

with edges = cube root of 512 = 8 cm each

8 by 8 by 8 cm, for length, width and height

wLh = 512

8^3 = 512

other possible integer values, with greater surface area, with volume =512 cm^3

are:

factors of 512 such

as

1 by 1 by 512

1 by 2 by 256

1 by 4 by 128

1 by 8 by 64

1 by 16 by 32

2 by 2 by 128

2 by 4 by 64

2 by 8 by 32

2 by 16 by 16

4 by 4 by 32

4 by 8 by 16

8 by 8 by 8 has surface area = 6 x 8 x8 = 384 cm^2

all other integer or non interger dimensions have larger surface are, up to infinity