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Delicious77 [7]
2 years ago
6

!!Plz urgent help!!

Mathematics
1 answer:
Firdavs [7]2 years ago
3 0

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 = \frac{1}{2}(\text{Base})(\text{Height})

                                             = \frac{1}{2}(AB)(BC)

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 = \frac{1}{2}(5)(12)

                                             = 30 cm²

Height of the triangular prism = 18 cm

Volume of the triangular prism = 30 × 18

                                                   = 540 cm³

Volume of one spherical bead = \frac{4}{3}\pi r^{3}

                                                   = \frac{4}{3}\pi (0.525)^{3}

                                                   = 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.

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