Answer:
Diameter of each cone \[(d)=3.5\,cm\] Radius of each cone \[(r)=\frac{3.5}{2}=\frac{7}{4}cm\] \[\left[ \because \,\,r=\frac{d}{2} \right]\] Height of each cone \[(h)=3\,\,cm\] Volume of 504 cones \[=504\times \text{Volume of one cone}\] \[=504\times \frac{1}{3}\pi {{r}^{2}}h\] \[=504\times \frac{1}{3}\times \frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times 3\] Let radius of sphere be R cm \[\therefore \] Volume of sphere = Volume of 504 cones \[\frac{4}{3}\times \frac{22}{7}\times {{R}^{3}}=504\times \frac{1}{3}\times \frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times 3\] \[R=\sqrt[3]{\frac{3\times 3\times 7\times 7\times 7\times 3}{2\times 2\times 2}}\] \[R=\frac{21}{2}cm\] Hence, diameter of sphere\[=2R=21cm\]. Now, surface area of sphere \[=4\pi {{R}^{2}}\] \[=4\times \frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\] \[=63\times 22\] \[=1386\,\,c{{m}^{2}}\] Hence, surface area of sphere is \[1386\text{ }c{{m}^{2}}\].
You need to login to perform this action.
You will be redirected in
3 sec