The ratio of the sides of 2 similar cube dis 3:4 the smaller cube has a volume of 729 Wat is the volume of the larger cube
volume of cubes is proportioanl to the cube of their corresponding sides
so V/729 = 4^3/3^3
27V = 46656
V = 1728
notice the sides increased by a ratio of 4:3
and 1728/729 = 64/27 = 4^3 : 3^3
To find the volume of the larger cube, we need to calculate the ratio of the volumes of the two cubes and then multiply it by the volume of the smaller cube.
Since the ratio of the sides is 3:4, the ratio of the volumes is equal to the cube of the side ratio. In this case, the side ratio is 3:4, so the volume ratio is (3/4)^3 = 27/64.
Given that the volume of the smaller cube is 729, we can multiply it by the volume ratio to find the volume of the larger cube:
Volume of larger cube = Volume of smaller cube × Volume ratio
= 729 × (27/64)
= 729 × 27 / 64
= 19683 / 64
≈ 307.297.
Therefore, the volume of the larger cube is approximately 307.297 cubic units.