Answer :
Certainly! Let's explore the dimensions of two different rectangular prisms, each with a volume of 2,400 cubic centimeters.
### Prism 1:
1. Length (l1): 20 centimeters
2. Width (w1): 30 centimeters
3. Height (h1): 4 centimeters
4. Volume Calculation:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
[tex]\[ \text{Volume} = 20 \, \text{cm} \times 30 \, \text{cm} \times 4 \, \text{cm} = 2400 \, \text{cubic centimeters} \][/tex]
### Prism 2:
1. Length (l2): 10 centimeters
2. Width (w2): 15 centimeters
3. Height (h2): 16 centimeters
4. Volume Calculation:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
[tex]\[ \text{Volume} = 10 \, \text{cm} \times 15 \, \text{cm} \times 16 \, \text{cm} = 2400 \, \text{cubic centimeters} \][/tex]
### Visual Representation:
#### Drawing Prism 1:
- Front View: This will show a rectangle with a height of 4 cm and a width of 30 cm.
- Side View: This will show a rectangle with a height of 4 cm and a length of 20 cm.
- Top View: This will show a rectangle with a length of 20 cm and a width of 30 cm.
```
Front View
+------------------------------+
| |
| |
| Height 4 cm |
| |
| Width 30 cm |
+------------------------------+
Side View
+-------------------+
| |
| |
| |
| Height 4 cm |
| Length 20 cm |
+-------------------+
Top View
+------------------------------+
| |
| |
| |
| Width 30 cm |
| |
| |
| |
| Length 20 cm
+------------------------------+
```
#### Drawing Prism 2:
- Front View: This will show a rectangle with a height of 16 cm and a width of 15 cm.
- Side View: This will show a rectangle with a height of 16 cm and a length of 10 cm.
- Top View: This will show a rectangle with a length of 10 cm and a width of 15 cm.
```
Front View
+-------------------+
| |
| |
| |
| |
| | Height 16 cm
| |
| |
| |
| |
| Width 15 cm |
+-------------------+
Side View
+-----------+
| |
| |
| |
| | Height 16 cm
| Length 10 cm |
+-----------+
Top View
+-------------------+
| |
| |
| |
| Width 15 cm |
| |
| |
| |
| Length 10 cm
+-------------------+
```
Each prism is uniquely sized, yet both have the same volume of 2,400 cubic centimeters. This shows how different dimension combinations can yield the same volume for rectangular prisms.
### Prism 1:
1. Length (l1): 20 centimeters
2. Width (w1): 30 centimeters
3. Height (h1): 4 centimeters
4. Volume Calculation:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
[tex]\[ \text{Volume} = 20 \, \text{cm} \times 30 \, \text{cm} \times 4 \, \text{cm} = 2400 \, \text{cubic centimeters} \][/tex]
### Prism 2:
1. Length (l2): 10 centimeters
2. Width (w2): 15 centimeters
3. Height (h2): 16 centimeters
4. Volume Calculation:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
[tex]\[ \text{Volume} = 10 \, \text{cm} \times 15 \, \text{cm} \times 16 \, \text{cm} = 2400 \, \text{cubic centimeters} \][/tex]
### Visual Representation:
#### Drawing Prism 1:
- Front View: This will show a rectangle with a height of 4 cm and a width of 30 cm.
- Side View: This will show a rectangle with a height of 4 cm and a length of 20 cm.
- Top View: This will show a rectangle with a length of 20 cm and a width of 30 cm.
```
Front View
+------------------------------+
| |
| |
| Height 4 cm |
| |
| Width 30 cm |
+------------------------------+
Side View
+-------------------+
| |
| |
| |
| Height 4 cm |
| Length 20 cm |
+-------------------+
Top View
+------------------------------+
| |
| |
| |
| Width 30 cm |
| |
| |
| |
| Length 20 cm
+------------------------------+
```
#### Drawing Prism 2:
- Front View: This will show a rectangle with a height of 16 cm and a width of 15 cm.
- Side View: This will show a rectangle with a height of 16 cm and a length of 10 cm.
- Top View: This will show a rectangle with a length of 10 cm and a width of 15 cm.
```
Front View
+-------------------+
| |
| |
| |
| |
| | Height 16 cm
| |
| |
| |
| |
| Width 15 cm |
+-------------------+
Side View
+-----------+
| |
| |
| |
| | Height 16 cm
| Length 10 cm |
+-----------+
Top View
+-------------------+
| |
| |
| |
| Width 15 cm |
| |
| |
| |
| Length 10 cm
+-------------------+
```
Each prism is uniquely sized, yet both have the same volume of 2,400 cubic centimeters. This shows how different dimension combinations can yield the same volume for rectangular prisms.
