Question

jasmine made a structure using two six - sided cubes that connect at a vertex, as shown below.
she plans to paint the entire structure. what is the surface area, in square feet, that jasmine will paint?

Explanation:

Step1: Calculate the surface area of the larger cube

The surface area formula for a cube is \(S = 6a^{2}\), where \(a\) is the side - length. For the larger cube with \(a = 8\) ft, \(S_{1}=6\times8^{2}=6\times64 = 384\) square feet.

Step2: Calculate the surface area of the smaller cube

For the smaller cube with \(a = 5\) ft, \(S_{2}=6\times5^{2}=6\times25=150\) square feet.

Step3: Subtract the area of the two - overlapping faces

When the two cubes are joined, two faces (one from each cube) are not on the surface of the combined structure. The area of each overlapping face is \(5\times5\) (the area of a face of the smaller cube). The total area of the two overlapping faces is \(2\times5\times5 = 50\) square feet.

Step4: Calculate the total surface area of the combined structure

The total surface area \(S=S_{1}+S_{2}-50\). Substitute \(S_{1}=384\) and \(S_{2}=150\) into the formula: \(S = 384+150 - 50=484\) square feet.

Answer:

\(484\) square feet