Math, asked by balour13, 11 months ago

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

Answers

Answered by pranav9066
1

Step-by-step explanation:

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

hence found .

Answered by ishwarsinghdhaliwal
1

Let the edges of three cubes be 3x,4x and 5x respectively

Volume of cube = a³

Volume of three cubes = (3x)³+ (4x)³+ (5x)³

=27x³+64x³+125x³=216x³

Volume of new cube =Volume of three cubes

a³= 216x³

a= 6x ....(1)

Diagonal of new cube = 12√3 cm

we know

Length \:  of  \: diagonal  \: of \:  cube \:  =  \sqrt{3}  \:  a \\  \sqrt{3} a = 12 \sqrt{3}  \\ a = 12

Put the value of a= 12 in (1)

12=6x

X=2

Edges of first cube = 3x = 3×2= 6

Edges of second cube = 4x = 4×2= 8

Edges of Third cube = 5x = 5×2= 10

Therefore, the edges of three cubes are 6cm ,8cm and 10 cm

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