EST 48: volume of a solid

caspermonday wrote:EST 48:

What is the volume of rectangular solid?

(1) two adjacent faces of the solid have areas 15 and 24, respectively
(2) each of two opposite faces of the solid has area 40

Please explain

Note the surface areas for a rectangle solid are lb, bh, lh, where l, b and n are length, bredth and height respectively.


(1) Two adjacent faces have areas lb and lh (or any two from the above three surfaces).
lb = 15, lh = 24
b/h = 5/8
In other words, b = 5k, h = 8k, l = 3/k

we can't get lbh.

(2) here bh is given. Useless on its own.

Combining together, we can get lbh

(lbh)^2 = 15.24.40

C is the answer