Answer:
890 beads can be fitted in the triangular prism.
Step-by-step explanation:
If we can fill the spherical beads completely in the triangular prism,
Volume of the triangular prism = Volume of the spherical beads
Volume of triangular prism = Area of the triangular base × Height
From the picture attached,
Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(AB)(BC)[/tex]
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
(13)² = 5² + BC²
169 = 25 + BC²
BC² = 144
BC = 12
Area of the triangular base = [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Height of the triangular prism = 18 cm
Volume of the triangular prism = 30 × 18
= 540 cm³
Volume of one spherical bead = [tex]\frac{4}{3}\pi r^{3}[/tex]
= [tex]\frac{4}{3}\pi (0.525)^{3}[/tex]
= 0.606 cm³
Let there are 'n' beads in the triangular prism,
Volume of 'n' beads = Volume of the prism
540 = 0.606n
n = 890.90
n ≈ 890
Therefore, 890 beads can be fitted in the triangular prism.
