Question

three cubes of metals with edges 5 cm 4 cm and 3 cm respectively are melted to form a single cube find the lateral surface area of the new cubes so formed

Answer 1

volume of the new cube = sum of volumes of three cubes
a^3 = a1^3 +a2^3+a3^3
a^3 = 5^3+4^3+3^3
a^3 = 125+64+27
a^3 = 216
a = 6cm
edge of new cube = 6cm
lateral surface area of new cube = 4a^2 = 4×(6)^2 = 4×36 = 144 cm^2

Answer 2

volume of 1st cube=a^3​=5^3cm^3=125cm^3
volume of 2nd cube=4^3cm^3=64cm^3
volume of 3rd cube=3^3cm^3=27cm^3
Total volume of 3 cubes=125+64+27=216cm^3
Edge of big cube=3×√(216)=6cm
So,Lateral surface of cube=4a^2=4×6×6cm^2=144cm^2