Question

A rectangular prism has a length of 10 in., a width of 2 in., and a height of 3 1/2 in. The prism is filled with cubes that have edge lengths of 1/2 in.How many cubes are needed to fill the rectangular prism

Answer 1

Step-1: Find the volume of the rectangular prism.

• Volume of rectangular prism: LBH
• => Volume of rectangular prism: (10)(2)(3 1/2)
• => Volume of rectangular prism: (10)(2)(3.5)
• => Volume of rectangular prism: (2)(35)
• => Volume of rectangular prism: 70 in³

Step-2: Find the volume of the small cube.

• Volume of cube: L³
• => Volume of cube: (1/2)³
• => Volume of cube: (1³/2³)
• => Volume of cube: (1/8)

Step-3: Divide.

• 70 ÷ 1/8
• => 70 x 8
• => 560 cubes

Thus, 560 cubes are needed to fill the rectangular prism.