Question
Download Solution PDFA cone of height 8 cm and base radius 4 cm is carved from a rectangular block 8 cm × 6 cm × 4 cm when melted. The percentage of wasted material is approximately:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven data:
Cone: height (h) = 8 cm, radius (r) = 4 cm
Rectangular block: length = 8 cm, breadth = 6 cm, height = 4 cm
Concept Used:
The volume of a cone = 1/3πr2h,
the volume of a rectangular block = length × breadth × height.
The percentage waste = ((Volume of block - Volume of cone)/Volume of block) × 100%.
Calculation:
⇒ Volume of cone = 1/3π(4)2 × (8) = 134.041 cm3
⇒ Volume of block = 8 × 6 × 4 = 192 cm3
⇒ Waste = 192 - 134.041 = 57.959 cm3
⇒ Percentage waste = (57.959/192) × 100% ≈ 30%
Therefore, the approximate percentage of wood wasted is 30%.
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