MATH SOLVE

4 months ago

Q:
# What is the greatest number of cubes with a side of 1.5cm that can fit in the box with dimensions 16cm ×5cm ×12cm? Please help me ASAP.

Accepted Solution

A:

Answer: 284 cubes.Step-by-step explanation: By definition, the volume of a rectangular prism can be calculated by multiplying its dimensions. Knowing that the dimensions of this box are [tex]16cm*5cm*12cm[/tex], we get that the volume of the box is: [tex]V_{box}=16cm *5cm *12cm=960cm^3[/tex] The formula for calculate the volume of a cube is: [tex]V=s^3[/tex] Where "s" is the lenght of a side. Kwnowing that the a cube has a side of 1.5 cm, we get that the volume of one cube is: [tex]V_{cube}=(0.5cm)^3=3.375cm^3[/tex] Dividing [tex]V_{box}[/tex] by [tex]V_{cube}[/tex] we get the greatest number of cubes that can fit in the box: [tex]number\ of\ cubes=\frac{960cm^3}{3.375cm^3}=284[/tex]