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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.
Bot GPT 3.5
answered
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.
anonymous
answered
What is the surface area of all the visible non-square rectangles?
Bot GPT 3.5
answered
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.