Question

Two identical rectangular prisms and a cube are joined. Answer the questions to find the new solid’s surface area.

A figure formed by 2 rectangular prisms and 1 cube. The cube has side lengths 2 feet. One rectangular prism is connected to the left side of the cube and another is connected to the top of the cube. The rectangular prisms have length 5 feet and square sides with length 2 feet.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the new solid, we need to calculate the surface area of each individual shape and then add them together.

Surface area of the cube:
Since all sides of the cube have length 2 feet, the surface area of each face is 2*2 = 4 square feet. Since there are 6 faces on a cube, the total surface area of the cube is 6*4 = 24 square feet.

Surface area of one rectangular prism:
The rectangular prism has length 5 feet, width 2 feet, and height 2 feet. To find the surface area, we calculate the area of each face:

- The top and bottom faces: 5*2 = 10 square feet each
- The front and back faces: 5*2 = 10 square feet each
- The left and right faces: 2*2 = 4 square feet each

Adding all the areas together, the total surface area of one rectangular prism is 2(10 + 10 + 4) = 48 square feet.

Since both rectangular prisms are identical, the total surface area of both prisms is 2*48 = 96 square feet.

Now, adding the surface area of the cube and both rectangular prisms, we get:
24 (cube) + 96 (prisms) = 120 square feet

Therefore, the total surface area of the new solid formed by two rectangular prisms and one cube is 120 square feet.

Answer 2

What is the surface area of all the visible non-square rectangles?

Answer 3

[AI-generated answer — Bot GPT 3.5]

The new solid formed by two rectangular prisms and one cube has a total of 6 visible non-square rectangles:

- The front and back faces of the first rectangular prism: 5 feet by 2 feet
- The left and right faces of the first rectangular prism: 5 feet by 2 feet
- The front and back faces of the second rectangular prism: 2 feet by 2 feet
- The top and bottom faces of the second rectangular prism: 2 feet by 5 feet

To calculate the total surface area of all these visible non-square rectangles, we first find the surface area of each individual rectangle and then sum them up:

Front and back faces of the first rectangular prism:
Each rectangle has a surface area of 5 feet * 2 feet = 10 square feet. Multiplying this by 2 gives a total of 2 * 10 = 20 square feet.

Left and right faces of the first rectangular prism:
Each rectangle has a surface area of 5 feet * 2 feet = 10 square feet. Multiplying this by 2 gives a total of 2 * 10 = 20 square feet.

Front and back faces of the second rectangular prism:
Each rectangle has a surface area of 2 feet * 2 feet = 4 square feet. Multiplying this by 2 gives a total of 2 * 4 = 8 square feet.

Top and bottom faces of the second rectangular prism:
Each rectangle has a surface area of 2 feet * 5 feet = 10 square feet. Multiplying this by 2 gives a total of 2 * 10 = 20 square feet.

Adding up the surface areas of all the visible non-square rectangles:
20 (front and back faces of the first prism) + 20 (left and right faces of the first prism) + 8 (front and back faces of the second prism) + 20 (top and bottom faces of the second prism) = 68 square feet

Therefore, the total surface area of all the visible non-square rectangles is 68 square feet.