# Three cubes of a metal whose edges are in the ratio 3:4:5 are melted to form a single cube whose diagonal is 15root3 cm.find the edges of the three edges.

1
by NajwaMody

2015-05-11T12:25:15+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
GIVEN ;-

⇒ Edges of the three melted cubes in ratio are =  3 : 4 : 5

⇒ Diagonal of the new single cube after melting = 15√3

TO FIND ;-

⇒ Find the edges of the three cubes

SOL ;-

⇒ We dont know the value of the edges of three cubes , so let us take the value as x, therefore -

⇒ Edges of three cubes are = 3 x , 4 x , 5 x

So now let us first find the volume of cube using its formula -

⇒ Volume of cube = a ³

⇒ ( 3 x )³ , ( 4 x )³ , ( 5 x )³

⇒27 x³ , 64 x³ , 125 x³

Now we got the volume of each cube but we need the total volume , so wee need to add all the volume to get the result,,

Volume of three cubes   ⇒ ( 27 x³ +  64 x³ + 125 x³ )

⇒ 216 x³ cu . units is the total volume

But we dont know the  the edge of the cube  , so let us take this as ''y''

⇒Diagonal of the cube =  s√3

⇒ 15√3 = 15

Therefore the edge of the cube is 15 units.

Now we got the value of side of the new cube , so let us find the value of the new cube formed -

⇒ Volume of new cube = a³

⇒ (15)3

⇒  3375 cu. units
So now we can find the value of x,-

⇒ 216 x³ = 3375

⇒ x³      = (3375 / 216)

⇒    x     = 15/6 = 5/2 = 2.5

so x is equal to 2.5 unit

--------------------------------------------------------------------------------

Edges of the cube are -

⇒ 3 x = 3 × 2 .5 =  7.5 units

⇒ 4 x = 4 × 2.5  =  1 unit

⇒ 5 x = 5 × 2.5  =  1. 25 units

----------------------------------------------------------------------------------