Respuesta :
Answer:
96
Step-by-step explanation:
Given:
Length of edge of cube = 1/5
Measurement of prism = 2 2/5 x 3 1/5 x 2
= [tex]\frac{12}{5} \times \frac{16}{5} \times3[/tex]
Question asked :
How many cubes with edge length 1/5 fit in a prism ?
Solution:
Surface area of a cube = [tex]6a^{2}[/tex]
= [tex]6 \times\frac{1}{5} \times\frac{1}{5}[/tex]
= [tex]\frac{6}{25}[/tex]
Volume of prism = Lengh[tex]\times[/tex]breadth[tex]\times[/tex]height
= [tex]\frac{12}{5} \times \frac{16}{5} \times3[/tex]
= [tex]\frac{576}{25}[/tex]
Number of cubes fit in this prism = Volume of prism divided by Surface area of a cube
= [tex]\frac{576}{25}[/tex] [tex]\div[/tex] [tex]\frac{6}{25}[/tex]
= [tex]\frac{576}{25}[/tex] [tex]\times[/tex] [tex]\frac{25}{6}[/tex]
By cancelling 25 by 25 = [tex]\frac{576}{6} = 96[/tex] pieces of cubes
Thus, 96 pieces of cubes with edge length 1/5 fit in a 2 2/5 x 3 1/5 x 2 prism.
