If two cuboids are similar, it means they have the same shape but can be different in size. The ratio of the corresponding sides of similar objects is the same.
Let's denote the dimensions of cuboid A as follows:
Length of A: L_A
Width of A: W_A
Height of A: H_A
Let's denote the dimensions of cuboid B as follows:
Length of B: L_B
Width of B: W_B
Height of B: H_B
We know that the volume of a cuboid is given by:
Volume = Length × Width × Height
For cuboid A, we have:
Volume of A = L_A × W_A × H_A = 500 cm³
We're also given that the surface area of A is 15 cm². The formula for the surface area of a cuboid is:
Surface Area = 2(L × W + W × H + H × L)
So, for cuboid A:
2(L_A × W_A + W_A × H_A + H_A × L_A) = 15 cm²
Now, let's consider cuboid B. Since the cuboids are similar, their corresponding sides are proportional. Therefore, we can write:
(L_B / L_A) = (W_B / W_A) = (H_B / H_A)
Now, let's consider the surface area of cuboid B:
2(L_B × W_B + W_B × H_B + H_B × L_B) = 27 cm²
We have a system of equations to solve:
L_A × W_A × H_A = 500
2(L_A × W_A + W_A × H_A + H_A × L_A) = 15
2(L_B × W_B + W_B × H_B + H_B × L_B) = 27
L_B / L_A = W_B / W_A = H_B / H_A
We need to solve this system of equations to find the volume of cuboid B. Since the equations are somewhat complex, you may want to use a calculator or a symbolic math software to find the values of L_B, W_B, and H_B that satisfy all of these conditions. Once you have those values, you can calculate the volume of cuboid B using the formula for the volume.