Cuboids A and B are similar.The volume of cuboid A is 500cm3.Calculate the volume of cuboid B. surface area of A is 15 cm and surface area of B is 27 cm.

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.