Three smaller cubes with sides of 3, 4, and 5 cm are melted together to form a large cube. What is the ratio of the smaller cubes' total surface area to the larger cube's total surface area?

25 : 18

We know that,

Volume of cube = (side)³ 

Surface area of cube = 6(side)²

We have a concept,

Volume of larger cube = Volume of smaller cube 1 + Volume of smaller cube 2 + Volume of smaller cube 3

Volume of larger cube = (3)³ + (4)³ + (5)³ = 216 cm³ 

= (side)³  = 216 cm³ 

=(side)= 6 cm 

Sum of surface areas of cubes = 6(3)² + 6(4)² + 6(5)² = 6(50) = 300

Surface area of larger cube = 6(6)² = 216

Ratio = 300 : 216 = 25 : 18