To determine the dimensions of a right square prism that has a volume of 360 cubic units, we need to verify which of the given options yields a volume of 360 cubic units when multiplying the length, width, and height.
Let's go through each option step by step:
1. Option 1: 3 by 3 by 40
- Volume = length × width × height
- Volume = 3 × 3 × 40
- Volume = 9 × 40
- Volume = 360 cubic units
Hence, 3 by 3 by 40 is a valid option.
2. Option 2: 4 by 4 by 20
- Volume = length × width × height
- Volume = 4 × 4 × 20
- Volume = 16 × 20
- Volume = 320 cubic units
Hence, 4 by 4 by 20 is not a valid option.
3. Option 3: 5 by 5 by 14
- Volume = length × width × height
- Volume = 5 × 5 × 14
- Volume = 25 × 14
- Volume = 350 cubic units
Hence, 5 by 5 by 14 is not a valid option.
4. Option 4: 2.5 by 12 by 12
- Volume = length × width × height
- Volume = 2.5 × 12 × 12
- Volume = 2.5 × 144
- Volume = 360 cubic units
Hence, 2.5 by 12 by 12 is a valid option.
5. Option 5: 3.6 by 10 by 10
- Volume = length × width × height
- Volume = 3.6 × 10 × 10
- Volume = 3.6 × 100
- Volume = 360 cubic units
Hence, 3.6 by 10 by 10 is a valid option.
Thus, the three sets of dimensions that result in a volume of 360 cubic units are:
- 3 by 3 by 40
- 2.5 by 12 by 12
- 3.6 by 10 by 10
