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  • https://ukrayinska.libretexts.org/%D0%94%D0%BE%D0%BA%D0%BE%D0%BB%D0%B5%D0%B4%D0%B6%D0%BD%D0%B0_%D0%BE%D1%81%D0%B2%D1%96%D1%82%D0%B0/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F/09%3A_%D0%A2%D0%B2%D0%B5%D1%80%D0%B4%D1%96_%D1%84%D1%96%D0%B3%D1%83%D1%80%D0%B8/9.07%3A_%D0%9A%D0%BE%D0%BC%D0%BF%D0%BE%D0%B7%D0%B8%D1%82%D0%BD%D1%96_%D1%82%D0%B2%D0%B5%D1%80%D0%B4%D1%96_%D1%80%D0%B5%D1%87%D0%BE%D0%B2%D0%B8%D0%BD%D0%B8
    \(\begin{aligned} V_{cylinder}&= \pi 6^{2}(13)=468 \pi \\ V_{hemisphere}&=12(\dfrac{4}{3} \pi 6^{3})=144 \pi \\ V_{total}&=468 \pi +144 \pi =612 \pi \text{ in}^{3} \end{aligned}\) \(\begin{aligned}SA&...\(\begin{aligned} V_{cylinder}&= \pi 6^{2}(13)=468 \pi \\ V_{hemisphere}&=12(\dfrac{4}{3} \pi 6^{3})=144 \pi \\ V_{total}&=468 \pi +144 \pi =612 \pi \text{ in}^{3} \end{aligned}\) \(\begin{aligned}SA&=LA_{cylinder}+LA_{hemisphere}+A_{base\: circle} \\ &=2 \pi rh+\dfrac{1}{2}4 \pi r^{2}+ \pi r^{2} \\ &=2 \pi (6)(13)+2 \pi 6^{2}+ \pi 6^{2} \\ &=156 \pi +72 \pi +36 \pi \\ &=264 \pi in^{2}\end{aligned}\)