A rectangular prism has a base that measures 4 cm by 5cm and a height of 3cm. Cameron fills the prism with 1/2cm cubes. Which statement is true?
A. Cameron will use 80 on the bottom layer.
B. Cameron will use a total of 240 cubes to fill the rectangular prism.
C. The rectangular prism will have a perimeter of 36 centimeters along the base.
D.there will be 3 layers of cubes in the rectangular prism.
I see 2 out the 4 statements being correct.
I see only A as being true.
To find the number of cubes needed to fill the rectangular prism, we can calculate the volume of the prism and divide it by the volume of one cube.
1. Calculate the volume of the rectangular prism:
Volume = base area * height
Volume = (length * width) * height
In this case:
Volume = (4 cm * 5 cm) * 3 cm
= 20 cm² * 3 cm
= 60 cm³
2. Calculate the volume of one cube:
The cube measures 1 cm on each side, so its volume is:
Volume = side length * side length * side length
Volume = 1 cm * 1 cm * 1 cm
= 1 cm³
3. Divide the volume of the rectangular prism by the volume of one cube:
Number of cubes = Volume of prism / Volume of one cube
Number of cubes = 60 cm³ / 1 cm³
= 60
Therefore, the correct statement is:
Cameron will need 60 cubes to fill the rectangular prism.