A) \[\sqrt[3]{12}\,cm\]
B) \[\sqrt[3]{13}\,cm\]
C) \[\sqrt[3]{6}\,cm\]
D) \[\sqrt[3]{6}\,cm\]
Correct Answer: B
Solution :
[b] Here, \[\Delta \,AO'B'\] and \[\Delta \,AOB\]are similar, let 00' = h and OB' = r \[\therefore \] \[\frac{AO}{AO'}=\frac{OB}{O'B'}\] \[\Rightarrow \] \[\frac{9}{9-h}=\frac{3}{r}\] \[\Rightarrow \] \[3r=9-h\] \[\Rightarrow \] \[h=9-3r\] Now, volume of frustum = 44 \[\Rightarrow \] \[\frac{1}{3}\pi h\,({{R}^{2}}+{{r}^{2}}+Rr)=44\] \[\Rightarrow \] \[\frac{1}{3}\times \frac{22}{7}\times (9-3r)(9+{{r}^{2}}+3r)=44\] \[\Rightarrow \] \[(3-r)(9+{{r}^{2}}+3r)=2\times 7\] \[\Rightarrow \] \[{{3}^{3}}-{{r}^{3}}=14\] \[\Rightarrow \] \[{{r}^{3}}=27-14\] \[\Rightarrow \] \[{{r}^{3}}=13\] \[\Rightarrow \] \[r=\sqrt[3]{13}\,cm\] |
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