A carpenter creates a long beam in the shape of a right prism whose base is a right-angled triangle. The legs of the triangular base measure 0.6 m and 0.8 m. The beam is 4.5 m long. If the wood used has a density of 0.75 g/cm³, find the mass of the beam in kilograms. (Give your answer to two decimal places)
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Correct answer: A
Explanation
Given:
Sides of the right-angled triangle = 0.6 m, 0.8 m
Length of the beam = 4.5 m
Density = 0.75 g/cm³
According to the formula:
Area of a right-angled triangle = (1/2) × a × b
Volume of a prism = Base Area × Length
Mass = Density × Volume
Base Area = (1/2) × 0.6 × 0.8 = 0.24 m²
Volume = 0.24 × 4.5 = 1.08 m³
Unit Conversion:
1 m³ = 10⁶ cm³
Volume = 1.08 × 10⁶ cm³
Mass = 0.75 × 1.08 × 10⁶ = 810 kg