A box in the shape of a right prism has a triangular base with sides 13 cm, 14 cm, and 15 cm. The height of the box is 20 cm. If a packaging company charges ₹0.75 per cm³ to fill the box with granules, find the total cost.
Show answer & explanation
Correct answer: C
Explanation
Given:
Sides of the triangle = 13, 14, 15 cm
Height of the prism = 20 cm
Cost = ₹0.75 per cm³
By the formula:
Area of the triangle = √(s(s − a)(s − b)(s − c))
Volume of the prism = Base area × Height
s = (13 + 14 + 15) / 2 = 21
Area = √(21(21 − 13)(21 − 14)(21 − 15)) = 84 cm²
Volume = 84 × 20 = 1680 cm³
Total cost = 1680 × 0.75 = ₹1260