find the approximately the difference between the value of two cubes side 3 cm and 3.04 cm
Answers
Three metal cubes whose edges measure 3cm, 4cm and 5cm respectively are melted to form a single cube.
Let a,b and c be the side length of cubes with edges 3 cm,4 cm and 5 cm respectively.
Let l be the side length of new cube.
(i)
Volume of new cube = Sum of volume of all three cubes
=3
3
+4
3
+5
3
=27+64+125=216 cm
3
∴ Volume of new cube =216=l
3
⟹l=6 cm
(ii) Total surface area of the new cube
=6a
2
=6(6
2
)
=216 cm
2
(iii)
Total surface area of the first cube with edge 3cm
=6a
2
=6×9=54 cm
2
Total surface area of the 2
nd
cube with edge 4cm
=6b
2
=6×16=96 cm
2
Total surface area of the 3
rd
cube with edge 5cm
=6c
2
=6×25=150 cm
2
Sum of total surface area of these three cubes
=54+96+150
=300cm
2
The difference between the total surface area of the new cube and the sum of total surface areas of the original three cubes =300−216=84 cm
2
Hence, the difference is 84 cm
2
.