Question

3 cubes of metal whose edges are in the ratio 3:4:5 are melted down into a single cube whose diagonal is 12√3cm .find the edges of the 3 cubes

Answer 1

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

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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

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