A) 8.96 cm
B) 35.84 cm
C) 5.97 cm
D) 17.92 cm
Correct Answer: B
Solution :
(b): The volume in both the cases will be equal. Let the height of cone be = h \[4\times \frac{22}{7}\times {{(14)}^{3}}\times \frac{1}{3}=\frac{22}{7}\times {{\left( \frac{35}{2} \right)}^{2}}\times \frac{h}{3}\] \[\Rightarrow \] \[4{{(14)}^{3}}=h{{\left( \frac{35}{2} \right)}^{2}}\] \[\Rightarrow \] \[h=\frac{4\times 14\times 14\times 14\times 2\times 2}{35\times 35}\] \[=\] \[h=35.84\,\,cm\] (Mind of a mathematician; Students should remember figures like \[{{11}^{2}}=121,\,\,\,{{11}^{3}}=1331;\] \[{{12}^{2}}=144,\,\,\,{{12}^{3}}=1728\]and these should be at the tip of their tongue.)
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