Question

a cube of a metal of 6cm edge is melted and recast into a cubiod whose bas is 3.60×0.60cm. find height of cuboid and also find surface areas of cuboid and the cube

Answer 1

Given;-Length of the one side of cube is 6cm
dimensions of the cuboid;-
length = 3.60cm
breadth = 0.60cm
height = ?
Solution;- The cube is melted and have been
recast into a cuboid, means the
volume remains the same.
volume of = volume of
cube. cuboid .
( ĺ )³ = ĺbh
( 6 )³ =3.60 × 0.60 × h
216 = 2.16 ×h
h = 216
——
2.16
h = 100 cm.
Now,the surface area of cube
= ( 6ĺ ²)
= 6×6²
= 6×36
=216cm²
Also, the surface area of the cuboid
= 2( lb + lh + bh )
= 2( 3.60×0.60 + 3.60×100 + 0.60 × 100 )
= 2( 2.16 + 360 +60 )
= 2( 422.16 )
=844.32 cm².
Therefore, the height of the cuboid is 100 cm
surface area of the cube is 216cm²
and, surface area of the cuboid is
844.32cm².