Posted by **sree** on Wednesday, January 4, 2012 at 12:39pm.

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?

- on areas -
**Reiny**, Wednesday, January 4, 2012 at 1:36pm
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

**volume = xyz = 1 x 4 x 10 = 40**

check:

xy = 1x4 = 4

xz = 1x10 = 10

yz = 4x40 = 40

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