A) 20 cm
B) 25 cm
C) 10 cm
D) 15 cm
Correct Answer: A
Solution :
Let OC = h and AB = r Now, \[\Delta OAB\tilde{\ }\Delta OCD\] \[\frac{AB}{CD}=\frac{OA}{OC}\] \[\Rightarrow \] \[\frac{r}{CD}=\frac{30}{h}\] \[\Rightarrow \] \[CD=\frac{rh}{30}\] Volume of smaller cone \[=\frac{1}{27}\] (Volume of whole cone) \[\frac{1}{3}\pi {{(CD)}^{2}}h=\frac{1}{27}\times \frac{1}{3}\pi {{r}^{2}}\times 30\] \[27\times {{\left( \frac{rh}{30} \right)}^{2}}h={{r}^{2}}\times 30\,\,\Rightarrow {{h}^{3}}=\frac{30\times 30\times 30}{27}\] \[{{h}^{3}}=10\times 10\times 10\,\,\,\Rightarrow \,\,h=10\,cm.\] Required height, \[AC=30-10=20\text{ }cm~\]You need to login to perform this action.
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