Final answer:
To find the number of small cubes that will fit into the large cube, calculate the volume of each cube and divide.
Step-by-step explanation:
To find the number of small cubes that will fit into the large cube, we need to calculate the volume of the large cube and the volume of each small cube. The area of one surface of the large cube is given as 49 sq. cm. Since a cube has 6 equal faces, each face will have an area of 49/6 = 8.17 sq. cm. The length of each side of the large cube can be found by taking the square root of the surface area of one face, which is √8.17 = 2.86 cm.
The volume of the large cube can be found by cubing the length of each side, which is (2.86 cm)^3 = 23.51 cm³. The volume of each small cube is (0.7 cm)^3 = 0.343 cm³.
To find the number of small cubes that will fit into the large cube, we can divide the volume of the large cube by the volume of each small cube, which is 23.51 cm³ / 0.343 cm³ = 68.59. Since we can't have a fraction of a small cube, we round down to get the final answer of 68 small cubes.