A monument shaped like a square-based pyramid is placed on top of a cuboidal stone base (1.2 m × 1.2 m × 0.5 m). The pyramid has the same base and is 1.5 m tall. Find the total height of the monument and its total volume.
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Correct answer: B
Explanation
Given:
Dimensions of the cuboid = 1.2 m × 1.2 m × 0.5 m
Base of the pyramid = 1.2 m × 1.2 m
Height of the pyramid = 1.5 m
By formula:
Volume of the cuboid = l × b × h
Volume of the pyramid = (1/3) × base area × height
Total height of the monument = 0.5 + 1.5 = 2 m
Volume of the cuboid = 1.2 × 1.2 × 0.5 = 0.72 m³
Volume of the pyramid = (1/3) × (1.2 × 1.2) × 1.5 = 0.72 m³
Total volume = 0.72 + 0.72 = 1.44 m³
Total height = 2 m
Total volume = 1.44 m³