A right prism has a base that is a regular hexagon of side 6 cm. The height of the prism is 10 cm. A square cavity of side 2 cm is carved vertically through the center of the prism from top to bottom. Calculate the volume of the material remaining in the prism.
Show answer & explanation
Correct answer: B
Explanation
Given:
Side of regular hexagon = 6 cm
Height of prism = 10 cm
Side of square cavity = 2 cm
By formula:
Area of regular hexagon = (3√3/2)a²
Area of regular hexagon = (3√3/2) × 6² = 54√3
Volume of prism = base area × height
Volume of prism = 54√3 × 10 = 540√3
Volume of cuboid (cavity) = a²h
Volume of cavity = 2² × 10 = 40
Remaining volume = 540√3 − 40
= 540 × 1.732 − 40 = 895.3 cm³