Question : A solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percentage of the material is wasted in this process?
Option 1: 25
Option 2: 0
Option 3: 5
Option 4: 10
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Correct Answer: 25
Solution : Given: Height of the cone = 36 cm Radius of base = 9 cm Radius of cylinder = 9 cm Height = 9 cm The volume of cone = $\frac{1}{3} \pi r^2 h$ $=\frac{1}{3}\times \pi \times 9^2 \times 36=972\pi$ cm$^3$ Volume of cylinder = $\pi r^2 h$ $=\pi \times 9^2\times 9=729\pi$ cm$^3$ The volume of waste = volume of cone – volume of cylinder $=972\pi - 729\pi=243\pi$ The material wasted = $\frac{\text{volume of cone – volume of cylinder}}{\text{volume of cone}}\times100$ = $\frac{243\pi }{972\pi}\times 100=25$% Hence, the correct answer is 25.
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