19. Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively a

1.	19. Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively aremelted to form a single cube. Find the lateral surface area of the newcube formed.
Answer» Given : Three cubes of metal with edges 3 cm , 4 cm & 5 cm respectively are melted to form of SINGLE cube. To find : Lateral surface area of the NEW cube formed. Solution : EDGE of 1st cube = 3 cm Edge of 2nd cube = 4 cm Edge of 3rd cube = 5 cm Formula Used :- ${\boxed{\bold{Volume\:of\:cube=Edge^3}}}$ Then, ★ $\sf{Volume_{\:1st\:cube}=3^3\:cm^3}$ $\to\sf{Volume_{\:1st\:cube}=27\:cm^3}$ ★ $\sf{Volume_{\:2nd\:cube}=4^3\:cm^3}$ $\to\sf{Volume_{\:2nd\:cube}=64\:cm^3}$ ★ $\sf{Volume_{\:3rd\:cube}=5^3\:cm^3}$ $\to\sf{Volume_{\:3rd\:cube}=125\:cm^3}$ Then, Total volume of 3 cubes , = (27+64+125) cm³ = 216 cm³ 3 cubes are melted to from a single cube. Consider, Edge of new single cube = R cm Volume of new single cube = R³ cm³ A/Q, $\to\sf{R^3=216}$ $\to\sf{R^3=6^3}$ $\to\sf{R=6}$ Lateral surface area of new cube , = 4 × edge² = 4 × 6² cm² = 144 cm² Therefore,the lateral surface area of the new cube is 144 cm² .