Find the surface area of a rectangular prism whose length is 18 millimeters, height is 10 millimeters, and width is 2 millimeters.(1 point)
thats wrong
A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 5 cm. How many rectangles in the net will have the dimensions 6 cm×4 cm?
A rectangular prism has 6 faces, and each face is a rectangle. To find out how many rectangles in the net will have the dimensions 6 cm × 4 cm, we need to look at the net of the rectangular prism and count the number of rectangles with these dimensions.
The net of the rectangular prism can be drawn as follows:
```
+------+ +------+
/ | / | / | / |
/ | / | / | / |
+------+ / | +------+ / |
| | |/ | | | |/ |
| +------+ | +------+
| / | | | / | |
| / | | | / | |
| / +----+ | / +----+
```
In the above net, there are four rectangles with dimensions 6 cm × 4 cm, which are indicated by the following letters:
- A: The rectangle on the front face
- B: The rectangle on the back face
- C: The rectangle on the left face
- D: The rectangle on the right face
Therefore, there are 4 rectangles in the net that have the dimensions 6 cm × 4 cm.
Use Nets to Solve Rectangular Problems Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Use the image to answer the question.
A 3 D rectangular prism shows a base length of 7and one half inches. The width is 4 inches and the height is 2 and one half inches. The edges that are not visible are shown as dashed lines.
A rectangular prism has dimensions 712 in.×4 in.× 212 in. In the net of this prism, how many sides will be represented?
(1 point)
The net of a rectangular prism consists of 6 faces, and each face is a rectangle. To find out how many rectangles in the net will be represented for a rectangular prism with dimensions of 7 1/2 in. × 4 in. × 2 1/2 in., we need to look at the net of the rectangular prism and count the number of rectangles.
The net of the rectangular prism can be drawn as follows:
```
+-------+ +-------+
/ | / | / | / |
/ | / | / | / |
+-------+ | +-------+ |
| | | | | | | |
| +----|---+ | +----|---+
| / | / | / | /
| / | / | / | /
|/ |/ |/ |/
+-------+ +-------+
```
In the above net, there are 7 rectangles that will be represented after folding to form a rectangular prism of dimensions 7 1/2 in. × 4 in. × 2 1/2 in.
Therefore, the answer is 7.
Keira is wrapping up her air conditioner for the winter. She needs to determine how much shrink wrap will cover the air conditioner completely. If the dimensions of the air conditioner are 23’’ x 25’’ x 17’’, what is its surface area in square inches? Use a net to help you calculate your answer.
To calculate the surface area of the air conditioner, we first need to find the area of each face of the rectangular prism it forms. We can use a net to visualize the faces and calculate their areas.
```
+------------------------+
/| /|
/ | / |
+------------------------+ |
| | | |
| | | |
| | | |
| | | |
| +---------------------|--+
| / | /
|/ |/
+------------------------+
```
From the above net, the six faces of the air conditioner are:
- Front and back faces: 23 x 17 = 391 square inches (2 of these)
- Top and bottom faces: 25 x 17 = 425 square inches (2 of these)
- Left and right faces: 23 x 25 = 575 square inches (2 of these)
Therefore, the surface area of the air conditioner is:
2(391) + 2(425) + 2(575) = 782 + 850 + 1150 = 2782 square inches
Thus, Keira needs 2782 square inches of shrink wrap to cover the air conditioner completely.
Use Nets to Solve Rectangular Problems Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration shows two rectangles intersecting, one is oriented horizontally and the other is oriented vertically. Their dimensions are labeled are they are divided into segments. The dimensions of the horizontal rectangle are as follows: It is divided into four segments. The first segment is labeled 3 inches horizontal and 8 inches vertical. The second segment is labeled 6 inches horizontal. The third segment is the intersection common area and is not labeled. The fourth segment is 6 inches horizontal and 8 inches vertical. The dimensions of the vertical rectangle are as follows: It is divided into three segments. The top segment is labeled 3 inches horizontal and 6 inches vertical. The second segment is the intersection common area and is not labeled. The third segment is labeled 6 inches vertical.
A necklace comes in a jewelry box whose net is shown in this image. What is the surface area of the box?
(1 point)
The net of the jewelry box can be drawn as follows:
```
+------+ +------+
/ | / | / | / |
/ | / | / | / |
+------+ / | +------+ / |
| | |/ | | | |/ |
| +------+ | +------+
| / | | | / | |
| / | | | / | |
| / +----+ | / +----+
```
The dimensions of the horizontal rectangle are 18 in x 8 in and the dimensions of the vertical rectangle are 6 in x 9 in.
To find the surface area of the box, we need to calculate the area of each face and sum them up. From the net, we see that the box has six faces, each of which is a rectangle.
The front face has an area of 18 in x 6 in = 108 in²
The back face has the same dimensions as the front face, so its area is also 108 in².
The top and bottom faces have areas of 8 in x 9 in = 72 in² (2 of these).
The left and right faces have areas of 18 in x 9 in = 162 in² (2 of these).
Adding up all the areas, we get:
108 in² + 108 in² + 72 in² + 72 in² + 162 in² + 162 in² = 684 in²
Therefore, the surface area of the jewelry box is 684 square inches.
The surface area of a rectangular prism can be found using the formula:
Surface Area = 2lw + 2lh + 2wh
where l is the length, h is the height, and w is the width of the prism.
Substituting the given values, we get:
Surface Area = 2(18)(2) + 2(18)(10) + 2(2)(10)
Surface Area = 36 + 360 + 40
Surface Area = 436
Therefore, the surface area of the rectangular prism is 436 square millimeters.