A retangular prism has a base that measures 9cm by 8cm and a height of 5cm. How many cubes will Joan use to fill the retangular prism?
IF the size of the cubes is 1 cm³, then the number of cubes is equal to the volume in cm³.
If the size of the cubes is bigger than 1cm³, then it is not possible to build the prism with the larger cubes because the GCF of 8,9,5 is 1.
360 cubes. :)
To find the number of cubes needed to fill a rectangular prism, we need to calculate the volume of the prism and then divide it by the volume of a single cube.
Step 1: Calculate the volume of the rectangular prism.
The volume of a rectangular prism is given by the formula: Volume = length × width × height.
In this case, the length is 9 cm, the width is 8 cm, and the height is 5 cm. Plug these values into the formula:
Volume = 9 cm × 8 cm × 5 cm = 360 cm³.
Step 2: Calculate the volume of a single cube.
To find the volume of a cube, we need to know the length of one side. Since it is not provided in the question, we cannot calculate an exact number of cubes needed. However, assuming the cubes are standard and have a side length of 1 cm, we can proceed with that assumption.
The volume of a cube is given by the formula: Volume = side length × side length × side length.
In this case, the side length is 1 cm. Plug this value into the formula:
Volume = 1 cm × 1 cm × 1 cm = 1 cm³.
Step 3: Divide the volume of the prism by the volume of a single cube.
Divide the volume of the rectangular prism (360 cm³) by the volume of a single cube (1 cm³):
Number of cubes = 360 cm³ / 1 cm³ = 360 cubes.
Therefore, Joan will need 360 cubes to fill the rectangular prism.