Apply the technique of using nets. What is the surface area of the rectangular prism whose dimensions measure 7 inches by 3 inches by 11 inches? (1 point)
Responses
262 in.2
262 in squared
231 in.2
231 in squared
131 in.2
131 in squared
154 in.2
To find the surface area of a rectangular prism, you need to calculate the sum of the areas of all its faces.
A rectangular prism has six faces: a top face, a bottom face, a front face, a back face, a left face, and a right face.
To find the surface area, you can use nets, which are 2D representations of the 3D shape.
In this case, the dimensions of the rectangular prism are 7 inches by 3 inches by 11 inches.
To calculate the surface area, you need to find the area of each face.
The top and bottom faces have dimensions of 7 inches by 3 inches, so their combined area is 2 * 7 * 3 = 42 square inches.
The front and back faces have dimensions of 7 inches by 11 inches, so their combined area is 2 * 7 * 11 = 154 square inches.
The left and right faces have dimensions of 3 inches by 11 inches, so their combined area is 2 * 3 * 11 = 66 square inches.
Now, you can add up the areas of all the faces to find the total surface area:
42 + 154 + 66 = 262 square inches.
Therefore, the surface area of the rectangular prism is 262 in².
To find the surface area of a rectangular prism using nets, you need to unfold the three-dimensional shape into a two-dimensional net. A net is a two-dimensional representation of a three-dimensional shape formed by unfolding its faces along their edges.
First, let's identify the faces of the rectangular prism. A rectangular prism has six faces, and each face is a rectangle. The dimensions given are 7 inches by 3 inches by 11 inches.
To create the net, start by drawing a rectangle with dimensions 7 inches by 3 inches. This represents one face of the prism. Next, draw another rectangle adjacent to it, also with dimensions 7 inches by 3 inches. Repeat this step until you have created four rectangles, forming a long strip.
Now, draw two more rectangles above and below the strip. These rectangles should have dimensions 11 inches by 7 inches. Attach each end of the strip to these rectangles, completing the net of the rectangular prism.
To calculate the surface area, add up the areas of all the rectangles in the net. The net consists of two rectangles with dimensions 7 inches by 3 inches and three rectangles with dimensions 11 inches by 7 inches.
The areas of the rectangles are as follows:
- 2 rectangles: 7 inches (length) * 3 inches (width) = 21 square inches each.
- 3 rectangles: 11 inches (length) * 7 inches (width) = 77 square inches each.
Calculate the sum of the areas:
2 * 21 square inches + 3 * 77 square inches = 42 square inches + 231 square inches = 273 square inches.
Therefore, the correct surface area of the rectangular prism is 273 square inches.