A) 75%
B) 50%
C) 40%
D) 25%
Correct Answer: A
Solution :
Volume of the cone \[=\frac{1}{3}\pi {{r}^{2}}h=\frac{1}{3}\pi \times {{(15)}^{2}}\times 15\] \[=\frac{1}{3}\pi \times {{(15)}^{3}}c{{m}^{3}}\] Volume of the wooden sphere \[=\frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi \times {{(15)}^{3}}c{{m}^{3}}\] Wasted wood \[=\frac{4}{3}\pi \times {{(15)}^{3}}-\frac{1}{3}\pi {{(15)}^{3}}\] \[=\pi \times {{(15)}^{3}}c{{m}^{3}}\] \[\therefore \] Required percentage \[=\frac{\pi \times {{(15)}^{3}}}{\frac{4}{3}\pi {{(15)}^{3}}}\times 100=75%\]
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