Question

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

a right triangle ,whose sides are 15cm nd 20cm,is made to revlve about its hypotenuse. find the surface area of the double cone so formed.

Answer 1

let edges of three cubes as

3x  ,  4x  ,  5x

then  in new cube 

[tex]Diagonal of Cube = a\sqrt{3}

  thus 12 \sqrt{3} = a \sqrt{3}

  then a = 12[/tex]

if three cubes melted to a new cube then

(3x)³ + (4x)³ + (5x)³ = 12³

27x³ + 64x³ + 125x³  = 1728

216x³ = 1728

x³ = 8
x = 2
then edges of three cubes are

6cm  , 8cm  ,  10cm