Question
The total surface area of a square-based right pyramid
is 1536 m², of which 37.5% is the area of the base of the pyramid. What is the volume (in mᶟ) of this pyramid?Solution
Total surface area = 1536 m² Base area = 37.5% of 1536 = 576 m² Side of bases = √576 = 24 m Lateral surface area = 1536-576 = 960 m² Slant height = 2x24x L= 960 L = 20 m L2=h²+ (24/2)2 400 =h² + + 144 h2 =400-144=256 h = 16 m Volume = 1/3 ×area of base ×h =1/3 ×576×16 =3072m3.
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