Three metal cubes with edge 6cm, 8cm, and 10cm respectively are melted together and formed into a new cube. find the volume, surface area and diagonal of the new cube?
Answers
1) volume of new cube = sum of volume of all cube
volume of new cube= a^3+a^3+a^3
= 6^3+8^3+10^3=216+512+1000
volume= 1728cm^3
2) volume of cube=a^3
1728=a^3
√1728=a
12cm = a
surface area of cube = 6a^2
=6×12^2=6×144
= 864
3) diagonal of cube = √3a
= √3×12=√36
=6
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Step-by-step explanation:
volume of the new cube = sum of the volume of the three cubes
volume of the cube =(6^3+8^3+20^3)cucm
=(216+512+1000)cucm
=1728cucm
so the volume of the cube is 1728cucm
the side of the new cube is cube root of( 1728)cucm=12 cm
surface area of the cube is 6.side ^2sq cm
=6.12^2 sq cm
=864sqcm
diagonal if the cube =length of one side .√3cm
=12√3cm