Three cubes of metal whose edges are in the ratio 3: 4:5 are melted down into a
single cube whose diagonal is 1213 cm. Find the edges of three cubes.
Answers
Answer:
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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