Question

the surface area of the three faces having the same border of a cuboid are 4,10,40 sq.cm respectively. find the volume of the cuboid?

Answer 1

let the dimensions of the cube be x, y , and z
xy = 4, (#1)
xz=10 and (#2)
yz=40 (#3)

#1 ÷ #2 :
z/y = 5/2
y = 2z/5

In #3: yz=40 ---> (2/5)z^2 = 40
z^2 = 100
z = 10
then y = (2/5)(10)
y = 4
in #1
xy=4
4x = 4
x = 1

<b>volume = xyz = 1 x 4 x 10 = 40</b>

check:
xy = 1x4 = 4
xz = 1x10 = 10
yz = 4x40 = 40