The volume of a cylinder is 60 cubic centimeters. The radius of the cylinder is 2. What is the number of cubic centimeters in the volume of the sphere that circumscribes the cylinder?
+14903 The volume of a cylinder is 60 cubic centimeters. The radius of the cylinder is 2. What is the number of cubic centimeters in the volume of the sphere that circumscribes the cylinder?
Hello Guest!
\(\color{blue}V_{zyl}=\pi r^2h\\ h=\frac{V_{zyl}}{\pi r^2}=\frac{60\ cm^3}{\pi \cdot 2^2\ cm^2}\)
\(h=\frac{15\ cm}{\pi}\)
\(R^2=(\frac{h}{2})^2+r^2=\frac{225\ cm^2}{\pi ^2}+2^2\ cm^2\\ R^2 =26.797\ cm^2\\ \color{blue} R=5.1766\ cm\)
\(V_{sphere}=\frac{4}{3}\pi \cdot R^3=\frac{4}{3}\pi \cdot 5.1766^3\ cm^3\)
\(V_{sphere}=581.065\ cm^3\)
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