question_answer

A cone of height 9 cm and diameter of the base 18 cm is carved from a wooden solid sphere of radius 9cm. The percentage of wood wasted is

A)  55%    

B)         65%

C)  75%    

D)  60%

Correct Answer: C

Solution :

According to questions, Volume of sphere =\[\frac{4}{3}\pi {{r}^{3}}\] Cone = ABC, Circle = ABCD \[\,=\frac{4}{3}\times \frac{22}{7}\times 9\times 9\times 9\] \[=972\pi \,\,\text{c}{{\text{m}}^{\text{3}}}\] Volume of curved cone\[=\frac{1}{3}\pi {{r}^{2}}h\] \[=\frac{1}{3}\pi \times 9\times 9\times 9=243\pi =729\pi \,\,c{{m}^{3}}\] Wood wasted\[=972\pi -243\pi =729\pi \,\,c{{m}^{3}}\] \[\therefore \]Required percentage\[=\frac{729\pi }{972\pi }\times 100=75%\]